## Alpay, Daniel Aron

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 Author ID: alpay.daniel Published as: Alpay, Daniel; Alpay, D. Homepage: https://www.chapman.edu/our-faculty/daniel-alpay External Links: MGP · ORCID · Math-Net.Ru · dblp · GND
 Documents Indexed: 302 Publications since 1984, including 10 Books 18 Contributions as Editor · 1 Further Contribution Reviewing Activity: 14 Reviews Biographic References: 1 Publication Co-Authors: 86 Co-Authors with 302 Joint Publications 1,597 Co-Co-Authors
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### Co-Authors

 18 single-authored 46 Dijksma, Aad 44 Sabadini, Irene 42 Colombo, Fabrizio 37 Bolotnikov, Vladimir 30 Gohberg, Israel 21 Lewkowicz, Izchak 20 Jørgensen, Palle E. T. 20 Volok, Dan 17 Langer, Heinz 15 Shapiro, Michael V. 14 Rovnyak, James 13 Vinnikov, Victor L. 11 de Snoo, Hendrik S. V. 11 Dym, Harry 10 Loubaton, Philippe 10 Rodman, Leiba X. 9 Kimsey, David Patrick 9 Levanony, David 9 Peretz, Yossi 8 Dubi, Chen 8 Kaptanoglu, H. Turgay 8 Luna-Elizarrarás, María Elena 7 Ball, Joseph Anthony 7 Kirstein, Bernd 6 Azizov, Tomas Ya. 6 Dewilde, Patrick M. 6 Salomon, Guy 6 Struppa, Daniele Carlo 5 Attia, Haim 5 Diki, Kamal 4 Bruinsma, Piet 4 Kaashoek, Marinus Adriaan 4 Leblond, Juliette 4 Paiva, Ismael L. 4 Shoikhet, David 3 Abu-Ghanem, Khaled 3 Correa-Romero, Flor de María 3 Freydin, Boris 3 Mboup, Mamadou 3 Pinhas, Ariel 3 Qian, Tao 3 Sakhnovich, Alexander L. 3 Timoshenko, Olga A. 3 Vajiac, Mihaela B. 3 Wanjala, Gerald 2 Baratchart, Laurent 2 Cerejeiras, Paula 2 Constantinescu, Tiberiu 2 Fritzsche, Bernd 2 Gantner, Jonathan 2 Kähler, Uwe 2 Kaliuzhnyi-Verbovetzkyi, Dmitry S. 2 Kipnis, Alon 2 Lerer, Leonid Efimovich 2 Mel’nikov, Andreĭ Andreevich 2 Pinton, Stefano 2 Rakowski, Marek 2 Ran, André C. M. 2 Reich, Simeon 2 Sadosky, Cora 2 Schneider, Baruch 2 Tsekanovskii, Eduard R. 2 Yger, Alain 1 Behrndt, Jussi 1 Bozejko, Marek 1 Buursema, R. W. 1 Chevreuil, Antoine 1 Cohen, Nir 1 Duksma, A. 1 Gabriyelyan, Saak S. 1 Gombani, Andrea 1 Guido, Daniele 1 Khatskevich, Viktor Anatol’evich 1 Martziano, Itzik 1 Marziano, Itzik 1 Ohsawa, Takeo 1 Peretz, Ronen 1 Porat, Motke 1 Putinar, Mihai 1 Rubenstein, S. 1 Saitoh, Saburou 1 Sakhnovych, Lev Aronovych 1 Sauvageot, Jean-Luc 1 Seager, Ron 1 Shondin, Yuri 1 Vâjiac, Adrian I. 1 van der Ploeg, Jan 1 Vegulla, Prasad
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### Serials

 36 Integral Equations and Operator Theory 36 Linear Algebra and its Applications 19 Operator Theory: Advances and Applications 13 Journal of Functional Analysis 13 Comptes Rendus. Mathématique. Académie des Sciences, Paris 10 Journal of Mathematical Analysis and Applications 8 Proceedings of the American Mathematical Society 6 Opuscula Mathematica 5 Journal of Mathematical Physics 5 Archiv der Mathematik 5 Comptes Rendus de l’Académie des Sciences. Série I. Mathématique 4 Mathematische Nachrichten 4 Systems & Control Letters 4 Zeitschrift für Analysis und ihre Anwendungen 3 Numerical Functional Analysis and Optimization 3 Transactions of the American Mathematical Society 3 The Journal of Geometric Analysis 3 Stochastic Processes and their Applications 3 The Journal of Fourier Analysis and Applications 3 Analysis and Applications (Singapore) 3 Complex Variables and Elliptic Equations 2 Israel Journal of Mathematics 2 Journal d’Analyse Mathématique 2 Mathematical Methods in the Applied Sciences 2 Rocky Mountain Journal of Mathematics 2 Results in Mathematics 2 Journal of Operator Theory 2 Comptes Rendus de l’Académie des Sciences. Série I 2 Indagationes Mathematicae. New Series 2 Potential Analysis 2 Advances in Applied Clifford Algebras 2 Infinite Dimensional Analysis, Quantum Probability and Related Topics 2 Computational Methods and Function Theory 2 Journal of Applied Mathematics and Computing 2 Milan Journal of Mathematics 2 Journal of Analysis and Applications 2 Mediterranean Journal of Mathematics 2 Complex Analysis and Operator Theory 2 Analysis and Mathematical Physics 2 SpringerBriefs in Mathematics 1 Houston Journal of Mathematics 1 IEEE Transactions on Information Theory 1 Advances in Mathematics 1 Annales de l’Institut Fourier 1 Applied Mathematics and Computation 1 Calcolo 1 Illinois Journal of Mathematics 1 Indiana University Mathematics Journal 1 Journal of Computational and Applied Mathematics 1 Journal of Differential Equations 1 Michigan Mathematical Journal 1 Monatshefte für Mathematik 1 SIAM Journal on Control and Optimization 1 Advances in Applied Mathematics 1 Complex Variables. Theory and Application 1 Journal of Time Series Analysis 1 Acta Applicandae Mathematicae 1 Journal of Theoretical Probability 1 St. Petersburg Mathematical Journal 1 Bulletin des Sciences Mathématiques 1 Discrete and Continuous Dynamical Systems 1 ELA. The Electronic Journal of Linear Algebra 1 Positivity 1 International Journal of Applied Mathematics 1 Communications on Pure and Applied Analysis 1 Sampling Theory in Signal and Image Processing 1 Panoramas et Synthèses 1 SMF/AMS Texts and Monographs 1 Quantum Studies: Mathematics and Foundations
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### Fields

 210 Operator theory (47-XX) 131 Functions of a complex variable (30-XX) 126 Functional analysis (46-XX) 49 Systems theory; control (93-XX) 28 Several complex variables and analytic spaces (32-XX) 28 Probability theory and stochastic processes (60-XX) 22 Linear and multilinear algebra; matrix theory (15-XX) 21 Harmonic analysis on Euclidean spaces (42-XX) 19 General and overarching topics; collections (00-XX) 14 Ordinary differential equations (34-XX) 13 Quantum theory (81-XX) 11 Approximations and expansions (41-XX) 9 Real functions (26-XX) 8 Information and communication theory, circuits (94-XX) 5 History and biography (01-XX) 5 Numerical analysis (65-XX) 4 Commutative algebra (13-XX) 4 Special functions (33-XX) 4 Partial differential equations (35-XX) 4 Dynamical systems and ergodic theory (37-XX) 4 Sequences, series, summability (40-XX) 4 Integral transforms, operational calculus (44-XX) 4 Statistics (62-XX) 3 Difference and functional equations (39-XX) 3 Abstract harmonic analysis (43-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 2 Combinatorics (05-XX) 2 Number theory (11-XX) 2 Associative rings and algebras (16-XX) 2 Measure and integration (28-XX) 2 Potential theory (31-XX) 1 Field theory and polynomials (12-XX) 1 Group theory and generalizations (20-XX) 1 Integral equations (45-XX) 1 Global analysis, analysis on manifolds (58-XX)

### Citations contained in zbMATH Open

264 Publications have been cited 2,153 times in 844 Documents Cited by Year
Schur functions, operator colligations, and reproducing kernel Pontryagin spaces. Zbl 0879.47006
Alpay, Daniel; Dijksma, Aad; Rovnyak, James; de Snoo, Hendrik
1997
Slice hyperholomorphic Schur analysis. Zbl 1366.30001
Alpay, Daniel; Colombo, Fabrizio; Sabadini, Irene
2016
Reproducing kernel spaces and applications. Zbl 1021.00005
2003
Hilbert spaces of analytic functions, inverse scattering and operator models. I. Zbl 0558.47015
Alpay, Daniel; Dym, Harry
1984
The spectral theorem for quaternionic unbounded normal operators based on the $$S$$-spectrum. Zbl 1357.47022
Alpay, Daniel; Colombo, Fabrizio; Kimsey, David P.
2016
Schur functions and their realizations in the slice hyperholomorphic setting. Zbl 1258.47018
Alpay, Daniel; Colombo, Fabrizio; Sabadini, Irene
2012
Basics of functional analysis with bicomplex scalars, and bicomplex Schur analysis. Zbl 1319.46001
Alpay, Daniel; Luna-Elizarrarás, Maria Elena; Shapiro, Michael; Struppa, Daniele C.
2014
Pontryagin-de Branges-Rovnyak spaces of slice hyperholomorphic functions. Zbl 1281.30034
Alpay, Daniel; Colombo, Fabrizio; Sabadini, Irene
2013
On a new class of structured reproducing kernel spaces. Zbl 0813.46018
Alpay, Daniel; Dym, Harry
1993
Hilbert spaces of analytic functions, inverse scattering and operator models. II. Zbl 0558.47016
Alpay, Daniel; Dym, Harry
1985
On applications of reproducing kernel spaces to the Schur algorithm and rational J unitary factorization. Zbl 0594.46022
Alpay, Daniel; Dym, Harry
1986
The Schur algorithm, reproducing kernel spaces and system theory. Transl. from the French by Stephen S. Wilson. Zbl 1059.93001
Alpay, Daniel
2001
The Fock space in the slice hyperholomorphic setting. Zbl 1314.30092
Alpay, Daniel; Colombo, Fabrizio; Sabadini, Irene; Salomon, Guy
2014
Some remarks on reproducing kernel Krein spaces. Zbl 0810.46025
Alpay, Daniel
1991
Self-mappings of the quaternionic unit ball: multiplier properties, the Schwarz-Pick inequality, and the Nevanlinna-Pick interpolation problem. Zbl 1318.30075
2015
Rational hyperholomorphic functions in $$\mathbb R^4$$. Zbl 1077.30044
Alpay, Daniel; Shapiro, Michael; Volok, Dan
2005
A new resolvent equation for the $$S$$-functional calculus. Zbl 1354.47016
Alpay, Daniel; Colombo, Fabrizio; Gantner, Jonathan; Sabadini, Irene
2015
Some finite-dimensional backward-shift-invariant subspaces in the ball and a related interpolation problem. Zbl 1010.47012
Alpay, Daniel; Kaptanoğlu, H. Turgay
2002
Generalized $$Q$$-functions and Dirichlet-to-Neumann maps for elliptic differential operators. Zbl 1179.47041
Alpay, Daniel; Behrndt, Jussi
2009
Reproducing kernel quaternionic Pontryagin spaces. Zbl 1074.46017
Alpay, Daniel; Shapiro, Michael
2004
Realizations of slice hyperholomorphic generalized contractive and positive functions. Zbl 1335.47012
Alpay, Daniel; Colombo, Fabrizio; Lewkowicz, Izchak; Sabadini, Irene
2015
A class of Gaussian processes with fractional spectral measures. Zbl 1229.60042
Alpay, Daniel; Jorgensen, Palle; Levanony, David
2011
On reproducing kernel spaces, the Schur algorithm, and interpolation in a general class of domains. Zbl 0793.47010
Alpay, Daniel; Dym, Harry
1992
The spectral theorem for unitary operators based on the $$S$$-spectrum. Zbl 1342.35189
Alpay, Daniel; Colombo, Fabrizio; Kimsey, David P.; Sabadini, Irene
2016
Inverse spectral problem for differential operators with rational scattering matrix functions. Zbl 0819.47008
Alpay, D.; Gohberg, I.
1995
Interpolation problems, extensions of symmetric operators and reproducing kernel spaces. II. Zbl 0787.47013
Alpay, Daniel; Bruinsma, Piet; Dijksma, Aad; de Snoo, Henk
1991
The Schur algorithm, reproducing kernel spaces and system theory. (Algorithme de Schur, espaces à noyau reproduisant et théorie des systèmes.) Zbl 0946.93002
Alpay, Daniel
1998
Krein-Langer factorization and related topics in the slice hyperholomorphic setting. Zbl 1314.47036
Alpay, Daniel; Colombo, Fabrizio; Sabadini, Irene
2014
On free stochastic processes and their derivatives. Zbl 1296.60181
Alpay, Daniel; Jorgensen, Palle; Salomon, Guy
2014
Interpolation problems, extensions of symmetric operators and reproducing kernel spaces. I. Zbl 0737.47016
Alpay, Daniel; Bruinsma, Piet; Dijksma, Aad; de Snoo, Henk
1991
Perturbation of the generator of a quaternionic evolution operator. Zbl 1327.47035
Alpay, Daniel; Colombo, Fabrizio; Sabadini, Irene
2015
Lossless inverse scattering and reproducing kernels for upper triangular operators. Zbl 0727.47005
Alpay, Daniel; Dewilde, Patrick; Dym, Harry
1990
A realization theorem for rational functions of several complex variables. Zbl 1157.93341
Alpay, D.; Dubi, C.
2003
On discrete analytic functions: products, rational functions and reproducing kernels. Zbl 1295.30107
Alpay, Daniel; Jorgensen, Palle; Seager, Ron; Volok, Dan
2013
Spectral theory for Gaussian processes: reproducing kernels, boundaries, and $$\mathrm{L}^{2}$$-wavelet generators with fractional scales. Zbl 1335.60053
Alpay, Daniel; Jorgensen, Palle
2015
Stochastic processes induced by singular operators. Zbl 1260.60137
Alpay, Daniel; Jorgensen, Palle E. T.
2012
On the reproducing kernel Hilbert spaces associated with the fractional and bi-fractional Brownian motions. Zbl 1136.46022
Alpay, Daniel; Levanony, David
2008
Finite dimensional de Branges spaces on Riemann surfaces. Zbl 1038.46020
Alpay, Daniel; Vinnikov, Victor
2002
A theorem of Beurling-Lax type for Hilbert spaces of functions analytic in the unit ball. Zbl 1046.46022
Alpay, D.; Dijksma, A.; Rovnyak, J.
2003
de Branges–Rovnyak spaces and Schur functions: The hyperholomorphic case. (Espaces de Branges Rovnyak et fonctions de Schur: Le cas hyper-analytique.) Zbl 1063.46019
Alpay, Daniel; Shapiro, Michael; Volok, Dan
2004
Some extremal problems linked with identification from partial frequency data. Zbl 0792.93022
Alpay, Daniel; Baratchart, Laurent; Leblond, Juliette
1993
Krein systems and canonical systems on a finite interval: Accelerants with a jump discontinuity at the origin and continuous potentials. Zbl 1206.34025
Alpay, D.; Gohberg, I.; Kaashoek, M. A.; Lerer, L.; Sakhnovich, A. L.
2010
The $$H^{\infty}$$ functional calculus based on the $$S$$-spectrum for quaternionic operators and for $$n$$-tuples of noncommuting operators. Zbl 1350.47017
Alpay, Daniel; Colombo, Fabrizio; Qian, Tao; Sabadini, Irene
2016
Moment problems in an infinite number of variables. Zbl 1336.44004
Alpay, Daniel; Jorgensen, Palle E. T.; Kimsey, David P.
2015
On a new class of reproducing kernel spaces and a new generalization of the Iohvidov laws. Zbl 0807.46026
Alpay, Daniel; Dym, Harry
1993
Linear stochastic systems: a white noise approach. Zbl 1217.93157
Alpay, Daniel; Levanony, David
2010
Reproducing kernel spaces of series of Fueter polynomials. Zbl 1107.46023
Alpay, Daniel; Shapiro, Michael; Volok, Dan
2006
The two-sided residue interpolation in the Stieltjes class of matrix functions. Zbl 0854.15009
Alpay, Daniel; Ball, Joseph A.; Gohberg, Israel; Rodman, Leiba
1994
Inverse spectral problems for difference operators with rational scattering matrix function. Zbl 0816.47006
Alpay, Daniel; Gohberg, Israel
1994
Realization and factorization for rational matrix functions with symmetries. Zbl 0735.15011
Alpay, Daniel; Ball, Joseph A.; Gohberg, Israel; Rodman, Leiba
1990
Functions of the infinitesimal generator of a strongly continuous quaternionic group. Zbl 1370.47015
Alpay, Daniel; Colombo, Fabrizio; Gantner, Jonathan; Kimsey, David P.
2017
The Schur algorithm and reproducing kernel Hilbert spaces in the ball. Zbl 1015.47008
Alpay, Daniel; Bolotnikov, Vladimir; Kaptanoğlu, H. Turgay
2002
On some operator colligations and associated reproducing kernel Hilbert spaces. Zbl 0794.47006
1993
Inverse problems associated to a canonical differential system. Zbl 0991.34070
Alpay, Daniel; Gohberg, Israel
2001
Two-sided interpolation for matrix functions with entries in the Hardy space. Zbl 0828.15025
1995
On a new class of realization formulas and their application. Zbl 0858.15012
Alpay, Daniel; Dym, Harry
1996
On the characteristics of a class of Gaussian processes within the white noise space setting. Zbl 1197.60037
Alpay, Daniel; Attia, Haim; Levanony, David
2010
Matrix-$$J$$-unitary non-commutative rational formal power series. Zbl 1110.47008
Alpay, D.; Kaliuzhnyi-Verbovetzkyi, D. S.
2006
An extension of Herglotz’s theorem to the quaternions. Zbl 1297.30073
Alpay, Daniel; Colombo, Fabrizio; Kimsey, David P.; Sabadini, Irene
2015
Direct and inverse scattering problem for canonical systems with a strictly pseudo-exponential potential. Zbl 0958.34069
Alpay, D.; Gohberg, I.; Kaashoek, M. A.; Sakhnovich, A. L.
2000
Some Krein spaces of analytic functions and an inverse scattering problem. Zbl 0638.46018
Alpay, Daniel
1987
Gleason’s problem and homogeneous interpolation in Hardy and Dirichlet-type spaces of the ball. Zbl 1022.47010
Alpay, Daniel; Kaptanoğlu, H. Turgay
2002
Rational functions and realization theory: The hyperholomorphic case. (Fonctions rationnelles et théorie de la réalisation: le cas hyper-analytique.) Zbl 1058.30041
Alpay, Daniel; Schneider, Baruch; Shapiro, Michael; Volok, Dan
2003
Interpolation problems, extensions of symmetric operators and reproducing kernel spaces. II. Zbl 0780.47016
Alpay, Daniel; Bruinsma, Piet; Dijksma, Aad; De Snoo, Henk
1992
On tangential interpolation in reproducing kernel Hilbert modules and applications. Zbl 0931.46024
Alpay, D.; Bolotnikov, V.
1997
Representation formulas for Hardy space functions through the Cuntz relations and new interpolation problems. Zbl 1316.41001
Alpay, Daniel; Jorgensen, Palle; Lewkowicz, Izchak; Marziano, Itzik
2013
Adaptive orthonormal systems for matrix-valued functions. Zbl 1370.47011
Alpay, Daniel; Colombo, Fabrizio; Qian, Tao; Sabadini, Irene
2017
The transformation of Issai Schur and related topics in an indefinite setting. Zbl 1128.47015
Alpay, D.; Dijksma, A.; Langer, H.
2007
The positive real lemma and construction of all realizations of generalized positive rational functions. Zbl 1231.93021
Alpay, Daniel; Lewkowicz, Izchak
2011
Indefinite Hardy spaces on finite bordered Riemann surfaces. Zbl 0952.30035
Alpay, Daniel; Vinnikov, Victor
2000
Schur algorithm in the class $${\mathcal{SI}}$$ of $$J$$-contractive functions intertwining solutions of linear differential equations. Zbl 1282.47010
Alpay, Daniel; Melnikov, Andrey; Vinnikov, Victor
2012
A Schur algorithm for transfer function of over-determined conservative systems, invariant in one direction. (Un algorithme de Schur pour les fonctions de transfert des systèmes surdéterminés invariants dans une direction.) Zbl 1169.47009
Alpay, Daniel; Melnikov, Andrey; Vinnikov, Victor
2009
Linear stochastic state space theory in the white noise space setting. Zbl 1214.93102
Alpay, Daniel; Levanony, David; Pinhas, Ariel
2010
Inner product spaces and Krein spaces in the quaternionic setting. Zbl 1376.46017
Alpay, Daniel; Colombo, Fabrizio; Sabadini, Irene
2015
On the equivalence of probability spaces. Zbl 1388.60081
Alpay, Daniel; Jorgensen, Palle; Levanony, David
2017
Time-varying signal approximation and estimation. Zbl 0722.93045
Alpay, D.; Dewilde, P.
1990
Non-commutative stochastic distributions and applications to linear systems theory. Zbl 1306.46046
Alpay, Daniel; Salomon, Guy
2013
Holomorphic operators between Krein spaces and the number of squares of associated kernels. Zbl 0790.47028
Alpay, D.; Dijksma, A.; van der Ploeg, J.; de Snoo, H. S. V.
1992
Some finite-dimensional backward shift-invariant subspaces in the ball and a related factorization problem. (Sous-espaces de codimension finie dans la boule unité et un problème de factorisation.) Zbl 0968.46020
Alpay, Daniel; Kaptanoğlu, H. Turgay
2000
On some operator colligations and associated reproducing kernel Pontryagin spaces. Zbl 0923.47007
Alpay, D.; Bolotnikov, V.; Duksma, A.; de Snoo, H.
1996
Inverse scattering problem for differential operators with rational scattering matrix functions. Zbl 0882.34082
Alpay, D.; Gohberg, I.
1996
A Hilbert space approach to bounded analytic extension in the ball. Zbl 1045.32015
Alpay, Daniel; Putinar, Mihai; Vinnikov, Victor
2003
Carathéodory functions in the Banach space setting. Zbl 1132.47009
Alpay, Daniel; Timoshenko, Olga; Volok, Dan
2007
Boundary interpolation and rigidity for generalized Nevanlinna functions. Zbl 1210.47040
Alpay, Daniel; Dijksma, Aad; Langer, Heinz; Reich, Simeon; Shoikhet, David
2010
Adaptative decomposition: the case of the Drury-Arveson space. Zbl 06829778
Alpay, Daniel; Colombo, Fabrizio; Qian, Tao; Sabadini, Irene
2017
Relative reproducing kernel Hilbert spaces. Zbl 1311.46024
Alpay, Daniel; Jorgensen, Palle; Volok, Dan
2014
Subclasses of Herglotz-Nevanlinna matrix-valued functions and linear systems. Zbl 1301.30035
Alpay, Daniel; Tsekanovskiĭ, Eduard
2001
Basic classes of matrices with respect to quaternionic indefinite inner product spaces. Zbl 1102.15014
Alpay, D.; Ran, A. C. M.; Rodman, L.
2006
Quaternionic de Branges spaces and characteristic operator function. Zbl 1475.47001
Alpay, Daniel; Colombo, Fabrizio; Sabadini, Irene
2020
On the differential structure of matrix-valued rational inner functions. Zbl 0810.93015
Alpay, Daniel; Baratchart, Laurent; Gombani, Andrea
1994
On the tangential interpolation problem for $$H_ 2$$ functions. Zbl 0808.47012
Alpay, Daniel; Bolotnikov, Vladimir; Peretz, Yossi
1995
Rational functions associated with the white noise space and related topics. Zbl 1203.30051
Alpay, Daniel; Levanony, David
2008
Integral formulas for a sub-Hardy Hilbert space on the ball with complete Nevanlinna-Pick reproducing kernel. Zbl 0993.32005
Alpay, Daniel; Kaptanoğlu, H. Turgay
2001
One two-sided residue interpolation for matrix-valued $$H_ 2$$-functions with symmetries. Zbl 0876.47013
Alpay, D.; Bolotnikov, V.; Loubaton, Ph.
1996
Factorization of $$J$$-unitary matrix polynomials on the line and a Schur algorithm for generalized Nevanlinna functions. Zbl 1073.47507
Alpay, D.; Dijksma, A.; Langer, H.
2004
On orthogonal matrix polynomials. Zbl 0659.47019
Alpay, Daniel; Gohberg, Israel
1988
An easy-to-compute factorization of rational generalized positive functions. Zbl 1208.30051
Alpay, Daniel; Lewkowicz, Izchak
2010
Interpolation problems for certain classes of slice hyperholomorphic functions. Zbl 1353.30049
2016
Extending wavelet filters: infinite dimensions, the nonrational case, and indefinite inner product spaces. Zbl 1311.65176
Alpay, Daniel; Jorgensen, Palle; Lewkowicz, Izchak
2013
Toeplitz operators on Arveson and Dirichlet spaces. Zbl 1144.47022
Alpay, Daniel; Kaptanoğlu, H. Turgay
2007
Discrete analytic Schur functions. Zbl 1486.30131
Alpay, Daniel; Volok, Dan
2022
Superoscillations and analytic extension in Schur analysis. Zbl 1462.30050
Alpay, Daniel; Colombo, Fabrizio; Sabadini, Irene
2021
Krein reproducing kernel modules in Clifford analysis. Zbl 1486.30132
Alpay, Daniel; Cerejeiras, Paula; Kähler, Uwe
2021
Quaternionic de Branges spaces and characteristic operator function. Zbl 1475.47001
Alpay, Daniel; Colombo, Fabrizio; Sabadini, Irene
2020
de Branges spaces on compact Riemann surfaces and a Beurling-Lax type theorem. Zbl 07243318
Alpay, Daniel; Pinhas, Ariel; Vinnikov, Victor
2020
Realizations of holomorphic and slice hyperholomorphic functions: the Krein space case. Zbl 1462.47010
Alpay, Daniel; Colombo, Fabrizio; Sabadini, Irene
2020
Pseudo-contractions, rigidity, fixed points and related questions. Zbl 1434.30006
Alpay, Daniel; Bolotnikov, Vladimir; Shoikhet, David
2020
A general setting for functions of Fueter variables: differentiability, rational functions, Fock module and related topics. Zbl 1439.30074
Alpay, Daniel; Paiva, Ismael L.; Struppa, Daniele C.
2020
On slice polyanalytic functions of a quaternionic variable. Zbl 1426.30034
Alpay, Daniel; Diki, Kamal; Sabadini, Irene
2019
About a non-standard interpolation problem. Zbl 1419.32002
Alpay, Daniel; Yger, Alain
2019
Distribution spaces and a new construction of stochastic processes associated with the Grassmann algebra. Zbl 1418.46028
Alpay, Daniel; Paiva, Ismael L.; Struppa, Daniele C.
2019
Corrigendum to “Notes on interpolation in the generalized Schur class. II: Nudel’man’s problem”. Zbl 1435.47023
Alpay, D.; Dijksma, A.; Rovnyak, J.
2019
Composition of rational functions: state-space realization and applications. Zbl 07106828
Alpay, Daniel; Lewkowicz, Izchak
2019
The Fock space as a de Branges-Rovnyak space. Zbl 1443.46017
Alpay, Daniel; Colombo, Fabrizio; Sabadini, Irene
2019
Positive and generalized positive real lemma for slice hyperholomorphic functions. Zbl 1417.30042
Alpay, Daniel; Colombo, Fabrizio; Lewkowicz, Izchak; Sabadini, Irene
2019
Positivity, rational Schur functions, Blaschke factors, and other related results in the Grassmann algebra. Zbl 1417.30043
Alpay, Daniel; Paiva, Ismael L.; Struppa, Daniele C.
2019
$$W$$-Markov measures, transfer operators, wavelets and multiresolutions. Zbl 1398.37020
Alpay, Daniel; Jorgensen, Palle; Lewkowicz, Izchak
2018
Herglotz functions of several quaternionic variables. Zbl 1393.30037
Abu-Ghanem, Khaled; Alpay, Daniel; Colombo, Fabrizio; Lewkowicz, Izchak; Sabadini, Irene
2018
Gleason’s problem, rational functions and spaces of left-regular functions: the split-quaternion setting. Zbl 1405.30050
Alpay, Daniel; Luna-Elizarrarás, María E.; Shapiro, Michael; Struppa, Daniele
2018
Generalized Fock spaces and the Stirling numbers. Zbl 1394.30039
Alpay, Daniel; Porat, Motke
2018
Gleason’s problem associated to a real ternary algebra and applications. Zbl 1405.30049
Alpay, D.; Vajiac, A.; Vajiac, M. B.
2018
“Wrong” side interpolation by positive real rational functions. Zbl 1380.26014
Alpay, Daniel; Lewkowicz, Izchak
2018
Functions of the infinitesimal generator of a strongly continuous quaternionic group. Zbl 1370.47015
Alpay, Daniel; Colombo, Fabrizio; Gantner, Jonathan; Kimsey, David P.
2017
Adaptive orthonormal systems for matrix-valued functions. Zbl 1370.47011
Alpay, Daniel; Colombo, Fabrizio; Qian, Tao; Sabadini, Irene
2017
On the equivalence of probability spaces. Zbl 1388.60081
Alpay, Daniel; Jorgensen, Palle; Levanony, David
2017
Adaptative decomposition: the case of the Drury-Arveson space. Zbl 06829778
Alpay, Daniel; Colombo, Fabrizio; Qian, Tao; Sabadini, Irene
2017
On a class of quaternionic positive definite functions and their derivatives. Zbl 1361.60026
Alpay, Daniel; Colombo, Fabrizio; Sabadini, Irene
2017
Kolmogorov’s axioms for probabilities with values in hyperbolic numbers. Zbl 1388.60011
Alpay, Daniel; Luna-Elizarrarás, M. Elena; Shapiro, Michael
2017
Beurling-Lax type theorems in the complex and quaternionic setting. Zbl 1368.47008
2017
Characterizations of families of rectangular, finite impulse response, para-unitary systems. Zbl 1409.93022
Alpay, Daniel; Jorgensen, Palle; Lewkowicz, Izchak
2017
Gleason’s problem associated to the fractional Cauchy-Riemann operator, Fueter series, Drury-Arveson space and related topics. Zbl 1375.30064
Alpay, D.; Cerejeiras, P.; Kähler, U.
2017
Slice hyperholomorphic Schur analysis. Zbl 1366.30001
Alpay, Daniel; Colombo, Fabrizio; Sabadini, Irene
2016
The spectral theorem for quaternionic unbounded normal operators based on the $$S$$-spectrum. Zbl 1357.47022
Alpay, Daniel; Colombo, Fabrizio; Kimsey, David P.
2016
The spectral theorem for unitary operators based on the $$S$$-spectrum. Zbl 1342.35189
Alpay, Daniel; Colombo, Fabrizio; Kimsey, David P.; Sabadini, Irene
2016
The $$H^{\infty}$$ functional calculus based on the $$S$$-spectrum for quaternionic operators and for $$n$$-tuples of noncommuting operators. Zbl 1350.47017
Alpay, Daniel; Colombo, Fabrizio; Qian, Tao; Sabadini, Irene
2016
Interpolation problems for certain classes of slice hyperholomorphic functions. Zbl 1353.30049
2016
A new realization of rational functions, with applications to linear combination interpolation, the Cuntz relations and kernel decompositions. Zbl 1337.30048
Alpay, Daniel; Jorgensen, Palle; Lewkowicz, Izchak; Volok, Dan
2016
Characterizations of rectangular (para)-unitary rational functions. Zbl 1376.26013
Alpay, Daniel; Jorgensen, Palle; Lewkowicz, Izchak
2016
Quaternion-valued positive definite functions on locally compact abelian groups and nuclear spaces. Zbl 1410.47008
Alpay, Daniel; Colombo, Fabrizio; Kimsey, David P.; Sabadini, Irene
2016
Wiener algebra for the quaternions. Zbl 1377.46034
Alpay, Daniel; Colombo, Fabrizio; Kimsey, David P.; Sabadini, Irene
2016
A complex analysis problem book. 2nd edition. Zbl 1356.30001
Alpay, Daniel
2016
Self-mappings of the quaternionic unit ball: multiplier properties, the Schwarz-Pick inequality, and the Nevanlinna-Pick interpolation problem. Zbl 1318.30075
2015
A new resolvent equation for the $$S$$-functional calculus. Zbl 1354.47016
Alpay, Daniel; Colombo, Fabrizio; Gantner, Jonathan; Sabadini, Irene
2015
Realizations of slice hyperholomorphic generalized contractive and positive functions. Zbl 1335.47012
Alpay, Daniel; Colombo, Fabrizio; Lewkowicz, Izchak; Sabadini, Irene
2015
Perturbation of the generator of a quaternionic evolution operator. Zbl 1327.47035
Alpay, Daniel; Colombo, Fabrizio; Sabadini, Irene
2015
Spectral theory for Gaussian processes: reproducing kernels, boundaries, and $$\mathrm{L}^{2}$$-wavelet generators with fractional scales. Zbl 1335.60053
Alpay, Daniel; Jorgensen, Palle
2015
Moment problems in an infinite number of variables. Zbl 1336.44004
Alpay, Daniel; Jorgensen, Palle E. T.; Kimsey, David P.
2015
An extension of Herglotz’s theorem to the quaternions. Zbl 1297.30073
Alpay, Daniel; Colombo, Fabrizio; Kimsey, David P.; Sabadini, Irene
2015
Inner product spaces and Krein spaces in the quaternionic setting. Zbl 1376.46017
Alpay, Daniel; Colombo, Fabrizio; Sabadini, Irene
2015
Gleason’s problem and Schur multipliers in the multivariable quaternionic setting. Zbl 1307.30087
Abu-Ghanem, Khaled; Alpay, Daniel; Colombo, Fabrizio; Sabadini, Irene
2015
An advanced complex analysis problem book. Topological vector spaces, functional analysis, and Hilbert spaces of analytic functions. Zbl 1350.46001
Alpay, Daniel
2015
On algebras which are inductive limits of Banach spaces. Zbl 1333.46048
Alpay, Daniel; Salomon, Guy
2015
Infinite product representations for kernels and iterations of functions. Zbl 1376.46020
Alpay, Daniel; Jorgensen, Palle; Lewkowicz, Izchak; Martziano, Itzik
2015
Boundary interpolation for slice hyperholomorphic Schur functions. Zbl 1317.30047
Abu-Ghanem, Khaled; Alpay, Daniel; Colombo, Fabrizio; Kimsey, David P.; Sabadini, Irene
2015
Schur analysis in the quaternionic setting: the Fueter regular and the slice regular case. Zbl 1337.47015
Alpay, Daniel; Colombo, Fabrizio; Sabadini, Irene
2015
Wiener chaos approach to optimal prediction. Zbl 1334.60057
Alpay, Daniel; Kipnis, Alon
2015
Realizations of infinite products, Ruelle operators and wavelet filters. Zbl 1326.42040
Alpay, Daniel; Jorgensen, Palle; Lewkowicz, Izchak
2015
Operator theory. With 51 figures and 2 tables. In 2 volumes. Zbl 1325.47001
2015
Basics of functional analysis with bicomplex scalars, and bicomplex Schur analysis. Zbl 1319.46001
Alpay, Daniel; Luna-Elizarrarás, Maria Elena; Shapiro, Michael; Struppa, Daniele C.
2014
The Fock space in the slice hyperholomorphic setting. Zbl 1314.30092
Alpay, Daniel; Colombo, Fabrizio; Sabadini, Irene; Salomon, Guy
2014
Krein-Langer factorization and related topics in the slice hyperholomorphic setting. Zbl 1314.47036
Alpay, Daniel; Colombo, Fabrizio; Sabadini, Irene
2014
On free stochastic processes and their derivatives. Zbl 1296.60181
Alpay, Daniel; Jorgensen, Palle; Salomon, Guy
2014
Relative reproducing kernel Hilbert spaces. Zbl 1311.46024
Alpay, Daniel; Jorgensen, Palle; Volok, Dan
2014
Generalized quaternionic Schur functions in the ball and half-space and Krein-Langer factorization. Zbl 1314.30091
Alpay, Daniel; Colombo, Fabrizio; Sabadini, Irene
2014
On some notions of convergence for $$n$$-tuples of operators. Zbl 1322.47011
Alpay, Daniel; Colombo, F.; Sabadini, I.
2014
Reproducing kernel Hilbert spaces generated by the binomial coefficients. Zbl 1332.46035
Alpay, Daniel; Jorgensen, Palle
2014
Interpolation by polynomials with symmetries. Zbl 1301.41001
Alpay, Daniel; Lewkowicz, Izchak
2014
Pontryagin-de Branges-Rovnyak spaces of slice hyperholomorphic functions. Zbl 1281.30034
Alpay, Daniel; Colombo, Fabrizio; Sabadini, Irene
2013
On discrete analytic functions: products, rational functions and reproducing kernels. Zbl 1295.30107
Alpay, Daniel; Jorgensen, Palle; Seager, Ron; Volok, Dan
2013
Representation formulas for Hardy space functions through the Cuntz relations and new interpolation problems. Zbl 1316.41001
Alpay, Daniel; Jorgensen, Palle; Lewkowicz, Izchak; Marziano, Itzik
2013
Non-commutative stochastic distributions and applications to linear systems theory. Zbl 1306.46046
Alpay, Daniel; Salomon, Guy
2013
Extending wavelet filters: infinite dimensions, the nonrational case, and indefinite inner product spaces. Zbl 1311.65176
Alpay, Daniel; Jorgensen, Palle; Lewkowicz, Izchak
2013
Parametrizations of all wavelet filters: input-output and state-space. Zbl 1346.94013
Alpay, Daniel; Jorgensen, Palle; Lewkowicz, Izchak
2013
Topological convolution algebras. Zbl 1275.46031
Alpay, Daniel; Salomon, Guy
2013
Convex cones of generalized positive rational functions and the Nevanlinna-Pick interpolation. Zbl 1303.47019
Alpay, Daniel; Lewkowicz, Izchak
2013
A generalized white noise space approach to stochastic integration for a class of Gaussian stationary increment processes. Zbl 1274.60223
Alpay, Daniel; Kipnis, Alon
2013
Schur functions and their realizations in the slice hyperholomorphic setting. Zbl 1258.47018
Alpay, Daniel; Colombo, Fabrizio; Sabadini, Irene
2012
Stochastic processes induced by singular operators. Zbl 1260.60137
Alpay, Daniel; Jorgensen, Palle E. T.
2012
Schur algorithm in the class $${\mathcal{SI}}$$ of $$J$$-contractive functions intertwining solutions of linear differential equations. Zbl 1282.47010
Alpay, Daniel; Melnikov, Andrey; Vinnikov, Victor
2012
White noise based stochastic calculus associated with a class of Gaussian processes. Zbl 1255.60117
Alpay, Daniel; Attia, Haim; Levanony, David
2012
A Schur transformation for functions in a general class of domains. Zbl 1254.30029
Alpay, Daniel; Dijksma, Aad; Langer, Heinz; Volok, Dan
2012
An interpolation problem for functions with values in a commutative ring. Zbl 1256.93096
Alpay, Daniel; Attia, Haim
2012
Quaternionic Hilbert spaces and a von Neumann inequality. Zbl 1301.47020
Alpay, Daniel; Kaptanoğlu, H. Turgay
2012
New topological $$\mathbb C$$-algebras with applications in linear systems theory. Zbl 1254.46002
Alpay, Daniel; Salomon, Guy
2012
A class of Gaussian processes with fractional spectral measures. Zbl 1229.60042
Alpay, Daniel; Jorgensen, Palle; Levanony, David
2011
The positive real lemma and construction of all realizations of generalized positive rational functions. Zbl 1231.93021
Alpay, Daniel; Lewkowicz, Izchak
2011
A complex analysis problem book. Zbl 1226.00001
Alpay, Daniel
2011
On the structure of the Taylor series in Clifford and quaternionic analysis. Zbl 1250.30046
Alpay, Daniel; Correa-Romero, Flor de María; Luna-Elizarrarás, María Elena; Shapiro, Michael
2011
Krein systems and canonical systems on a finite interval: Accelerants with a jump discontinuity at the origin and continuous potentials. Zbl 1206.34025
Alpay, D.; Gohberg, I.; Kaashoek, M. A.; Lerer, L.; Sakhnovich, A. L.
2010
Linear stochastic systems: a white noise approach. Zbl 1217.93157
Alpay, Daniel; Levanony, David
2010
On the characteristics of a class of Gaussian processes within the white noise space setting. Zbl 1197.60037
Alpay, Daniel; Attia, Haim; Levanony, David
2010
Linear stochastic state space theory in the white noise space setting. Zbl 1214.93102
Alpay, Daniel; Levanony, David; Pinhas, Ariel
2010
Boundary interpolation and rigidity for generalized Nevanlinna functions. Zbl 1210.47040
Alpay, Daniel; Dijksma, Aad; Langer, Heinz; Reich, Simeon; Shoikhet, David
2010
An easy-to-compute factorization of rational generalized positive functions. Zbl 1208.30051
Alpay, Daniel; Lewkowicz, Izchak
2010
Discrete-time multi-scale systems. Zbl 1286.94029
2010
Generalized $$Q$$-functions and Dirichlet-to-Neumann maps for elliptic differential operators. Zbl 1179.47041
Alpay, Daniel; Behrndt, Jussi
2009
A Schur algorithm for transfer function of over-determined conservative systems, invariant in one direction. (Un algorithme de Schur pour les fonctions de transfert des systèmes surdéterminés invariants dans une direction.) Zbl 1169.47009
Alpay, Daniel; Melnikov, Andrey; Vinnikov, Victor
2009
Schur multipliers and de Branges-Rovnyak spaces: the multiscale case. Zbl 1174.47017
Alpay, Daniel; Dijksma, Aad; Volok, Dan
2009
Rigidity theorems, boundary interpolation and reproducing kernels for generalized Schur functions. Zbl 1185.30040
Alpay, Daniel; Reich, Simeon; Shoikhet, David
2009
Krein systems. Zbl 1191.47061
Alpay, D.; Gohberg, I.; Kaashoek, M. A.; Lerer, L.; Sakhnovich, A.
2009
...and 164 more Documents
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### Cited by 633 Authors

 170 Alpay, Daniel Aron 69 Jørgensen, Palle E. T. 56 Sabadini, Irene 55 Colombo, Fabrizio 43 Bolotnikov, Vladimir 26 Dym, Harry 24 Dijksma, Aad 23 Arqub, Omar Abu 22 Sakhnovich, Alexander L. 20 Ball, Joseph Anthony 19 Cho, Ilwoo 19 Shapiro, Michael V. 18 Gohberg, Israel 18 Rodman, Leiba X. 17 Arov, Damir Zyamovich 17 Lewkowicz, Izchak 17 Vinnikov, Victor L. 16 Luna-Elizarrarás, María Elena 15 Tian, Feng 15 Volok, Dan 14 Qian, Tao 13 Derkach, Volodymyr Oleksandrovych 12 Al-Smadi, Mohammed H. 12 Gantner, Jonathan 12 Leblond, Juliette 12 Ren, Guangbin 12 Thirulogasanthar, Kengatharam 11 Kimsey, David Patrick 11 Muraleetharan, B. 10 Diki, Kamal 10 Mel’nikov, Andreĭ Andreevich 10 Momani, Shaher M. 9 Behrndt, Jussi 9 Derevyagin, Maxim S. 9 Dubi, Chen 9 Kaashoek, Marinus Adriaan 9 Kaptanoglu, H. Turgay 9 Staffans, Olof Johan 8 Belyi, Sergey V. 8 Constantinescu, Tiberiu 8 Fritzsche, Bernd 8 Geng, Fazhan 8 Kirstein, Bernd 8 Langer, Heinz 8 Loubaton, Philippe 8 Rovnyak, James 8 Tsekanovskii, Eduard R. 8 Woracek, Harald 7 Ghanmi, Allal 7 Levanony, David 7 Maayah, Banan 7 Ran, André C. M. 7 Struppa, Daniele Carlo 6 Bory Reyes, Juan 6 Dewilde, Patrick M. 6 Gheondea, Aurelian 6 McCarthy, John Edward 6 Partington, Jonathan R. 6 Pinton, Stefano 6 Shoikhet, David 6 Wang, Xieping 5 Baratchart, Laurent 5 Cui, Minggen 5 Gal, Sorin Gheorghe 5 Gesztesy, Fritz 5 Jury, Michael T. 5 Kaliuzhnyi-Verbovetskyi, Dmitry S. 5 Kumar, Romesh 5 Peretz, Yossi 5 Shalit, Orr Moshe 5 Tian, James F. 5 van der Veen, Alle-Jan 5 Xu, Li 4 Agler, Jim 4 Arlins’kyĭ, Yuriĭ Moĭseĭovych 4 Băleanu, Dumitru I. 4 Chen, Gongning 4 Ćurgus, Branko 4 de Snoo, Hendrik S. V. 4 Gombani, Andrea 4 González-Cervantes, José Óscar 4 Hu, Yongjian 4 Infusino, Maria 4 Kheifets, Alexander 4 Martin, Robert T. W. 4 Matsushita, Shinya 4 Michaletzky, Gyórgy 4 Paiva, Ismael L. 4 Salomon, Guy 4 Sarkar, Jaydeb 4 Xu, Zhenghua 4 Yan, Shi 4 Yger, Alain 4 Zhao, Dongdong 3 Abu-Ghanem, Khaled 3 Attia, Haim 3 Azizov, Tomas Ya. 3 Bezuglyi, Sergey I. 3 Bisi, Cinzia 3 Cerejeiras, Paula ...and 533 more Authors
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### Cited in 178 Serials

 85 Linear Algebra and its Applications 82 Integral Equations and Operator Theory 59 Complex Analysis and Operator Theory 42 Journal of Functional Analysis 35 Journal of Mathematical Analysis and Applications 30 Advances in Applied Clifford Algebras 20 Journal of Mathematical Physics 16 Complex Variables and Elliptic Equations 14 Mathematische Nachrichten 14 Comptes Rendus. Mathématique. Académie des Sciences, Paris 13 Transactions of the American Mathematical Society 12 Journal of Mathematical Sciences (New York) 11 Proceedings of the American Mathematical Society 11 The Journal of Geometric Analysis 9 Applied Mathematics and Computation 9 Analysis and Mathematical Physics 8 Journal of Differential Equations 8 Multidimensional Systems and Signal Processing 8 Opuscula Mathematica 7 Journal d’Analyse Mathématique 7 Journal of Geometry and Physics 7 Advances in Mathematics 7 Journal of Computational and Applied Mathematics 7 Systems & Control Letters 7 Analysis and Applications (Singapore) 6 Acta Applicandae Mathematicae 6 MCSS. Mathematics of Control, Signals, and Systems 6 Fractals 6 Computational Methods and Function Theory 6 Journal of Applied Mathematics and Computing 5 Indagationes Mathematicae. New Series 5 The Journal of Fourier Analysis and Applications 5 Milan Journal of Mathematics 4 Israel Journal of Mathematics 4 Mathematical Methods in the Applied Sciences 4 Ukrainian Mathematical Journal 4 Chaos, Solitons and Fractals 4 Archiv der Mathematik 4 Journal of Approximation Theory 4 Numerical Functional Analysis and Optimization 4 St. Petersburg Mathematical Journal 4 Filomat 4 Infinite Dimensional Analysis, Quantum Probability and Related Topics 4 Banach Journal of Mathematical Analysis 3 Linear and Multilinear Algebra 3 Rocky Mountain Journal of Mathematics 3 Results in Mathematics 3 Zeitschrift für Analysis und ihre Anwendungen 3 Applied Mathematics Letters 3 International Journal of Computer Mathematics 3 Stochastic Processes and their Applications 3 Potential Analysis 3 Abstract and Applied Analysis 3 Soft Computing 3 Discrete and Continuous Dynamical Systems. Series S 3 Journal of Spectral Theory 3 Mathematics 3 Advances in Operator Theory 2 American Mathematical Monthly 2 Applicable Analysis 2 Journal of the Franklin Institute 2 Reviews in Mathematical Physics 2 Automatica 2 Dissertationes Mathematicae 2 Illinois Journal of Mathematics 2 Indiana University Mathematics Journal 2 Mathematische Annalen 2 Journal of Time Series Analysis 2 Journal of Theoretical Probability 2 Applied and Computational Harmonic Analysis 2 Bulletin des Sciences Mathématiques 2 ELA. The Electronic Journal of Linear Algebra 2 Mathematical Problems in Engineering 2 Positivity 2 Annales Henri Poincaré 2 Mediterranean Journal of Mathematics 2 Advances in Difference Equations 2 Journal of Physics A: Mathematical and Theoretical 2 Journal of Nonlinear Science and Applications 2 Science China. Mathematics 2 Mathematical Sciences 2 Quantum Studies: Mathematics and Foundations 2 Special Matrices 2 European Journal of Mathematics 2 International Journal of Applied and Computational Mathematics 1 Analysis Mathematica 1 The Canadian Journal of Statistics 1 Communications in Algebra 1 Communications on Pure and Applied Mathematics 1 International Journal of Theoretical Physics 1 Physica A 1 Mathematics of Computation 1 Annales de l’Institut Fourier 1 The Annals of Probability 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 1 Calcolo 1 Functional Analysis and its Applications 1 Journal of Applied Probability 1 Journal of Number Theory 1 Journal für die Reine und Angewandte Mathematik ...and 78 more Serials
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### Cited in 52 Fields

 436 Operator theory (47-XX) 265 Functions of a complex variable (30-XX) 247 Functional analysis (46-XX) 84 Ordinary differential equations (34-XX) 82 Systems theory; control (93-XX) 74 Linear and multilinear algebra; matrix theory (15-XX) 71 Several complex variables and analytic spaces (32-XX) 64 Numerical analysis (65-XX) 60 Harmonic analysis on Euclidean spaces (42-XX) 60 Probability theory and stochastic processes (60-XX) 56 Partial differential equations (35-XX) 46 Quantum theory (81-XX) 32 Approximations and expansions (41-XX) 25 Number theory (11-XX) 25 Dynamical systems and ergodic theory (37-XX) 19 Information and communication theory, circuits (94-XX) 18 Integral transforms, operational calculus (44-XX) 18 Integral equations (45-XX) 17 Measure and integration (28-XX) 17 Potential theory (31-XX) 17 Statistics (62-XX) 16 Combinatorics (05-XX) 13 Real functions (26-XX) 11 Global analysis, analysis on manifolds (58-XX) 10 Difference and functional equations (39-XX) 7 Commutative algebra (13-XX) 7 Algebraic geometry (14-XX) 7 Nonassociative rings and algebras (17-XX) 7 Topological groups, Lie groups (22-XX) 7 Abstract harmonic analysis (43-XX) 6 Special functions (33-XX) 5 Associative rings and algebras (16-XX) 3 History and biography (01-XX) 3 Category theory; homological algebra (18-XX) 3 Sequences, series, summability (40-XX) 3 Computer science (68-XX) 3 Mechanics of deformable solids (74-XX) 2 Mathematical logic and foundations (03-XX) 2 Order, lattices, ordered algebraic structures (06-XX) 2 Field theory and polynomials (12-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Geometry (51-XX) 2 Differential geometry (53-XX) 2 General topology (54-XX) 2 Fluid mechanics (76-XX) 2 Classical thermodynamics, heat transfer (80-XX) 2 Statistical mechanics, structure of matter (82-XX) 2 Operations research, mathematical programming (90-XX) 1 Group theory and generalizations (20-XX) 1 Optics, electromagnetic theory (78-XX) 1 Relativity and gravitational theory (83-XX) 1 Biology and other natural sciences (92-XX)