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## Grünbaum, Francisco Alberto

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 Author ID: grunbaum.francisco-alberto Published as: Gruenbaum, F. A.; Gruenbaum, F. Alberto; Grünbaum, F.; Grünbaum, F. A.; Grünbaum, F. Alberto; Grünbaum, Francisco Alberto Homepage: https://math.berkeley.edu/people/faculty/f-alberto-gruenbaum External Links: MGP · GND
 Documents Indexed: 169 Publications since 1966, including 3 Books
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#### Co-Authors

 77 single-authored 13 Velázquez, Luis 11 Haine, Luc 11 Pacharoni, Inés 8 Duran, Antonio J. 7 Castro, Mirta M. 7 Tirao, Juan 5 Domínguez de la Iglesia, Manuel 5 Zurrián, Ignacio Nahuel 4 Vinet, Luc 4 Werner, Albert H. 4 Werner, Reinhard F. 4 Zhedanov, Alexei S. 3 Cantero, María José 3 Cedzich, Christopher 3 Matusevich, Laura Felicia 3 Moral, Leandro 3 Yakimov, Milen T. 3 Zubelli, Jorge P. 2 Auslander, Louis 2 Bertero, Mario 2 Hasenfeld, Andrew 2 Horozov, Emil Ivanov 2 Iliev, Plamen 2 Patch, Sarah K. 2 Rahman, Mizan 2 Zarantonello, Eduardo H. 1 Antoun, John T. 1 Bernfeld, Marvin 1 Blahut, Richard E. 1 Bourgain, Jean 1 Caputo, Jean-Guy 1 Casper, W. Riley 1 Davison, Mark E. 1 Duistermaat, Johannes Jisse 1 Feig, Ephraim 1 Geib, T. 1 Helton, John William 1 Kailath, Thomas 1 Khargoneka, P. 1 Kohn, Philip 1 Lardizabal, Carlos F. 1 Latham, Geoff A. 1 Longhi, L. G. S. 1 Machida, Takuya 1 Martínez-Finkelshtein, Andrei 1 McGrouther, Caroline 1 Mitter, S. J. 1 Moore, Calvin C. 1 Natterer, Frank 1 Pejic, Michael 1 Perlstadt, Marci A. 1 Singer, J. R. 1 Stahl, Christoph 1 Stahl, Clément 1 Tirao, Juan Alfredo 1 Wilkening, Jared
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#### Serials

 13 Inverse Problems 8 IMRN. International Mathematics Research Notices 7 Journal of Computational and Applied Mathematics 7 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 6 Communications in Mathematical Physics 6 Journal of Mathematical Analysis and Applications 4 Communications on Pure and Applied Mathematics 4 Journal of Physics A: Mathematical and General 4 Bulletin of the American Mathematical Society 3 Advances in Mathematics 3 Physica D 3 Linear Algebra and its Applications 3 SIAM Journal on Applied Mathematics 2 Journal of Mathematical Physics 2 Journal of Approximation Theory 2 Journal of Multivariate Analysis 2 Numerical Functional Analysis and Optimization 2 Proceedings of the American Mathematical Society 2 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 2 Advances in Applied Mathematics 2 SIAM Journal on Algebraic and Discrete Methods 2 Constructive Approximation 2 Proceedings of the National Academy of Sciences of the United States of America 2 Annales Henri Poincaré 2 Quantum Information Processing 2 The IMA Volumes in Mathematics and its Applications 2 Journal of Physics A: Mathematical and Theoretical 1 Archive for Rational Mechanics and Analysis 1 IMA Journal of Applied Mathematics 1 Letters in Mathematical Physics 1 Linear and Multilinear Algebra 1 Studia Mathematica 1 Reviews in Mathematical Physics 1 Annales de l’Institut Fourier 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Illinois Journal of Mathematics 1 Integral Equations and Operator Theory 1 Journal of Applied Probability 1 Journal of Functional Analysis 1 Michigan Mathematical Journal 1 Pacific Journal of Mathematics 1 Transactions of the American Mathematical Society 1 SIAM Journal on Matrix Analysis and Applications 1 International Journal of Mathematics 1 Indagationes Mathematicae. New Series 1 Experimental Mathematics 1 Applied and Computational Harmonic Analysis 1 St. Petersburg Mathematical Journal 1 Methods and Applications of Analysis 1 Bulletin des Sciences Mathématiques 1 The Ramanujan Journal 1 Mathematical Physics, Analysis and Geometry 1 Journal of Nonlinear Mathematical Physics 1 Internet Mathematics 1 Communications in Applied Mathematics and Computational Science 1 Acta Crystallographica. Section A 1 Random Matrices: Theory and Applications
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#### Fields

 58 Special functions (33-XX) 39 Probability theory and stochastic processes (60-XX) 34 Harmonic analysis on Euclidean spaces (42-XX) 26 Ordinary differential equations (34-XX) 24 Operator theory (47-XX) 22 Partial differential equations (35-XX) 21 Numerical analysis (65-XX) 18 Topological groups, Lie groups (22-XX) 18 Biology and other natural sciences (92-XX) 14 Linear and multilinear algebra; matrix theory (15-XX) 14 Quantum theory (81-XX) 12 Difference and functional equations (39-XX) 12 Integral transforms, operational calculus (44-XX) 10 Dynamical systems and ergodic theory (37-XX) 9 Statistical mechanics, structure of matter (82-XX) 8 Information and communication theory, circuits (94-XX) 7 Integral equations (45-XX) 6 Systems theory; control (93-XX) 4 General and overarching topics; collections (00-XX) 4 Abstract harmonic analysis (43-XX) 4 Fluid mechanics (76-XX) 3 Combinatorics (05-XX) 3 Nonassociative rings and algebras (17-XX) 3 Statistics (62-XX) 3 Optics, electromagnetic theory (78-XX) 2 Associative rings and algebras (16-XX) 2 Functional analysis (46-XX) 2 Geometry (51-XX) 2 Differential geometry (53-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Mathematical logic and foundations (03-XX) 1 Number theory (11-XX) 1 Algebraic geometry (14-XX) 1 Group theory and generalizations (20-XX) 1 Real functions (26-XX) 1 Functions of a complex variable (30-XX) 1 Approximations and expansions (41-XX) 1 Computer science (68-XX)

#### Citations contained in zbMATH

133 Publications have been cited 1,345 times in 626 Documents Cited by Year
Differential equations in the spectral parameter. Zbl 0625.34007
Duistermaat, J. J.; Grünbaum, F. A.
1986
Bispectral Darboux transformations: an extension of the Krall polynomials. Zbl 1125.37321
Grünbaum, F. Alberto; Haine, Luc
1997
Some functions that generalize the Krall-Laguerre polynomials. Zbl 0926.33007
Grünbaum, F. Alberto; Haine, Luc; Horozov, Emil
1999
Matrix-valued Szegő polynomials and quantum random walks. Zbl 1186.81036
Cantero, M. J.; Moral, L.; Grünbaum, F. Alberto; Velázquez, L.
2010
Orthogonal polynomials satisfying differential equations: The role of the Darboux transformation. Zbl 0865.33008
Grünbaum, F. Alberto; Haine, Luc
1996
Matrix valued spherical functions associated to the complex projective plane. Zbl 0996.43013
Grünbaum, F. A.; Pacharoni, I.; Tirao, J.
2002
Orthogonal matrix polynomials satisfying second-order differential equations. Zbl 1073.33009
Durán, Antonio J.; Grünbaum, F. Alberto
2004
The $$q$$-version of a theorem of Bochner. Zbl 0865.33012
Grünbaum, F. Alberto; Haine, Luc
1996
Matrix valued orthogonal polynomials of the Jacobi type. Zbl 1070.33011
Grünbaum, F. A.; Pacharoni, I.; Tirao, J.
2003
Matrix valued Jacobi polynomials. Zbl 1026.33008
Grünbaum, F. Alberto
2003
Variations on a theme of Heine and Stieltjes: An electrostatic interpretation of the zeros of certain polynomials. Zbl 0934.33012
Grünbaum, F. Alberto
1998
Discrete bispectral Darboux transformations from Jacobi operators. Zbl 1051.39020
Grünbaum, F. Alberto; Yakimov, Milen
2002
Propagation of chaos for the Boltzmann equation. Zbl 0236.45011
Grünbaum, F. Alberto
1971
Recurrence for discrete time unitary evolutions. Zbl 1276.81087
Grünbaum, F. A.; Velázquez, L.; Werner, A. H.; Werner, R. F.
2013
The algebra of differential operators associated to a weight matrix. Zbl 1120.33008
Grünbaum, F. Alberto; Tirao, Juan
2007
Differential operators commuting with finite convolution integral operators: Some non-Abelian examples. Zbl 0497.22012
Gruenbaum, F. A.; Longhi, L.; Perlstadt, M.
1982
The CGMV method for quantum walks. Zbl 1252.82082
Cantero, M. J.; Grünbaum, F. A.; Moral, L.; Velázquez, L.
2012
One-dimensional quantum walks with one defect. Zbl 1251.81026
Cantero, M. J.; Grünbaum, F. A.; Moral, L.; Velázquez, L.
2012
Structural formulas for orthogonal matrix polynomials satisfying second-order differential equations. I. Zbl 1097.42018
Durán, Antonio J.; Grünbaum, F. Alberto
2005
Matrix valued orthogonal polynomials of Jacobi type: the role of group representation theory. Zbl 1082.33006
Grünbaum, F. Alberto; Pacharoni, Inés; Tirao, Juan Alfredo
2005
Eigenvectors of a Toeplitz matrix: Discrete version of the prolate spheroidal wave functions. Zbl 0519.47019
Gruenbaum, F. Alberto
1981
Tomographic reconstruction with arbitrary directions. Zbl 0441.93031
Davison, M. E.; Grünbaum, F. Alberto
1981
The algebra of differential operators associated to a family of matrix-valued orthogonal polynomials: five instructive examples. Zbl 1130.33004
Castro, Mirta M.; Grünbaum, F. Alberto
2006
A survey on orthogonal matrix polynomials satisfying second order differential equations. Zbl 1060.42017
Durán, Antonio J.; Grünbaum, F. Alberto
2005
A matrix-valued solution to Bochner’s problem. Zbl 0990.22012
Grünbaum, F. A.; Pacharoni, I.; Tirao, J.
2001
The eigenvectors of the discrete Fourier transform: A version of the Hermite functions. Zbl 0516.65099
Gruenbaum, F. Alberto
1982
Quantum recurrence of a subspace and operator-valued Schur functions. Zbl 1296.37014
Bourgain, J.; Grünbaum, F. A.; Velázquez, L.; Wilkening, J.
2014
Toeplitz matrices commuting with tridiagonal matrices. Zbl 0477.15005
Gruenbaum, F. Alberto
1981
Tridiagonalization and the Heun equation. Zbl 1364.34126
Grünbaum, F. Alberto; Vinet, Luc; Zhedanov, Alexei
2017
The bispectral problem: An overview. Zbl 0999.47018
Grünbaum, F. Alberto
2001
A theorem of Bochner, revisited. Zbl 0868.35116
Grünbaum, F. Alberto; Haine, Luc
1997
Orthogonal matrix polynomials, scalar-type Rodrigues formulas and Pearson equations. Zbl 1066.42018
Durán, Antonio J.; Grünbaum, F. Alberto
2005
Commuting pairs of linear ordinary differential operators of orders four and six. Zbl 0654.47027
Grünbaum, F. Alberto
1988
A new property of reproducing kernels for classical orthogonal polynomials. Zbl 0562.33008
Grünbaum, F. Alberto
1983
Matrix valued orthogonal polynomials arising from group representation theory and a family of quasi-birth-and-death processes. Zbl 1163.60033
Grünbaum, F. Alberto; de la Iglesia, Manuel D.
2008
Orthogonal matrix polynomials satisfying first order differential equations: a collection of instructive examples. Zbl 1100.42015
Castro, Mirta M.; Grünbaum, F. Alberto
2005
Some bispectral musings. Zbl 0944.34062
Grünbaum, F. Alberto
1998
Time-band limiting and the bispectral problem. Zbl 0802.34086
Grünbaum, F. Alberto
1994
A study of Fourier space methods for ”limited angle” image reconstruction. Zbl 0458.65105
Grünbaum, F. Alberto
1980
Algebraic Heun operator and band-time limiting. Zbl 1405.33025
Grünbaum, F. Alberto; Vinet, Luc; Zhedanov, Alexei
2018
The Darboux process and a noncommutative bispectral problem: some explorations and challenges. Zbl 1263.34022
Grünbaum, F. Alberto
2011
Matrix orthogonal polynomials satisfying second-order differential equations: coping without help from group representation theory. Zbl 1221.42046
Durán, Antonio J.; Grünbaum, F. Alberto
2007
A characterization for a class of weight matrices with orthogonal matrix polynomials satisfying second-order differential equations. Zbl 1102.42013
Durán, Antonio J.; Grünbaum, F. Alberto
2005
Some functions that generalize the Askey-Wilson polynomials. Zbl 0871.33009
Grünbaum, F. Alberto; Haine, Luc
1997
Bulk-edge correspondence of one-dimensional quantum walks. Zbl 1342.82064
Cedzich, C.; Grünbaum, F. A.; Stahl, C.; Velázquez, L.; Werner, A. H.; Werner, R. F.
2016
An invitation to matrix-valued spherical functions: Linearization of products in the case of complex projective space $$P_2(\mathbb C)$$. Zbl 1075.33004
Grünbaum, F. Alberto; Pacharoni, Inés; Tirao, Juan
2004
Heat kernel expansions on the integers. Zbl 0996.35077
Grünbaum, F. Alberto; Iliev, Plamen
2002
A system of multivariable Krawtchouk polynomials and a probabilistic application. Zbl 1244.33003
Grünbaum, F. Alberto; Rahman, Mizan
2011
Random walks and orthogonal polynomials: some challenges. Zbl 1184.33004
Grünbaum, F. Alberto
2008
Matrix valued spherical functions associated to the three dimensional hyperbolic space. Zbl 1048.22005
Grünbaum, F. A.; Pacharoni, I.; Tirao, J.
2002
On a $$q$$-analogue of the string equation and a generalization of the classical orthogonal polynomials. Zbl 0938.33010
Grünbaum, F. Alberto; Haine, Luc
1999
Commuting differential operators for the finite Laplace transform. Zbl 0603.44002
Bertero, M.; Grünbaum, F. A.
1985
Properties of matrix orthogonal polynomials via their Riemann-Hilbert characterization. Zbl 1242.42020
Grünbaum, F. Alberto; De La Iglesia, Manuel D.; Martínez-Finkelshtein, Andrei
2011
Electrostatic interpretation for the zeros of certain polynomials and the Darboux process. Zbl 0989.42006
Grünbaum, F. Alberto
2001
On a family of 2-variable orthogonal Krawtchouk polynomials. Zbl 1220.33008
Grünbaum, F. Alberto; Rahman, Mizan
2010
Matrix-valued orthogonal polynomials related to $$\mathrm{SU}(N+1)$$, their algebras of differential operators, and the corresponding curves. Zbl 1149.33002
Grünbaum, F. Alberto; de la Iglesia, Manuel D.
2007
Special issue to celebrate Pierre Sabatier’s 65th birthday. Papers from the conference “RCP264: Inverse problems and nonlinearity—theory and applications”, Montpellier, France, June 20–24, 2000. Zbl 0988.00112
Bertero, Mario (ed.); Caputo, Jean Guy (ed.); Grünbaum, F. Alberto (ed.); Natterer, Frank (ed.)
2001
On the Krall-Hermite and the Krall-Bessel polynomials. Zbl 0910.33004
Grünbaum, F. Alberto; Haine, Luc; Horozov, Emil
1997
A new kind of inequality for Bessel functions. Zbl 0304.33012
Grünbaum, F. Alberto
1973
The square of a Gaussian process. Zbl 0244.60033
Grünbaum, F. Alberto
1972
Linearization for the Boltzmann equation. Zbl 0236.45012
Grünbaum, F. Alberto
1972
The topological classification of one-dimensional symmetric quantum walks. Zbl 1391.82027
Cedzich, C.; Geib, T.; Grünbaum, F. A.; Stahl, C.; Velázquez, L.; Werner, A. H.; Werner, R. F.
2018
A quantum dynamical approach to matrix Khrushchev’s formulas. Zbl 1371.30004
Cedzich, C.; Grünbaum, F. A.; Velázquez, L.; Werner, A. H.; Werner, R. F.
2016
The Darboux process and time-and-band limiting for matrix orthogonal polynomials. Zbl 1326.33013
Castro, M.; Grünbaum, F. A.
2015
Two stochastic models of a random walk in the $$\mathrm U(n)$$-spherical duals of $$U(n+1)$$. Zbl 1279.60010
Grünbaum, F. A.; Pacharoni, I.; Tirao, J.
2013
The Karlin-McGregor formula for a variant of a discrete version of Walsh’s spider. Zbl 1187.37094
Grünbaum, F. Alberto
2009
Matrix differential equations and scalar polynomials satisfying higher order recursions. Zbl 1163.42009
Durán, Antonio J.; Grünbaum, F. Alberto
2009
The prolate spheroidal phenomenon as a consequence of bispectrality. Zbl 1085.47056
Grünbaum, F. Alberto; Yakimov, Milen
2004
A noncommutative version of the bispectral problem. Zbl 1038.39012
Grünbaum, F. Alberto; Iliev, Plamen
2003
The use of higher-order invariants in the determination of generalized Patterson cyclotomic sets. Zbl 1176.82034
Grünbaum, F. Alberto; Moore, Calvin C.
1995
Differential operators commuting with convolution integral operators. Zbl 0506.45018
Grünbaum, F. Alberto
1983
A remark on Hilber’s matrix. Zbl 0484.15009
Gruenbaum, F. Alberto
1982
The Heisenberg inequality for the discrete Fourier transform. Zbl 1053.42009
Grünbaum, F. Alberto
2003
Band-time-band limiting integral operators and commuting differential operators. Zbl 0878.47031
Grünbaum, F. Alberto
1996
Diffuse tomography: The isotropic case. Zbl 0760.65109
Grünbaum, F. Alberto
1992
The Fourier transform and the discrete Fourier transform. Zbl 0674.65114
Auslander, Louis; Grünbaum, F. Alberto
1989
A property of Legendre polynomials. Zbl 0202.34301
Grünbaum, F. A.
1970
On the extension of uniformly continuous mappings. Zbl 0169.38801
Grünbaum, F.; Zarantonello, E. H.
1968
A further look at time-and-band limiting for matrix orthogonal polynomials. Zbl 1411.33008
Castro, M.; Grünbaum, F. A.; Pacharoni, I.; Zurrián, I.
2018
Stochastic LU factorizations, Darboux transformations and urn models. Zbl 1402.60090
Grünbaum, F. Alberto; de la Iglesia, Manuel D.
2018
Time and band limiting for matrix valued functions: an integral and a commuting differential operator. Zbl 1367.47078
Grünbaum, F. A.; Pacharoni, I.; Zurrián, I.
2017
Time and band limiting for matrix valued functions, an example. Zbl 1318.33018
Grünbaum, F. Alberto; Pacharoni, Inés; Zurrián, Ignacio Nahuel
2015
Birth and death processes and quantum spin chains. Zbl 1285.82028
Grünbaum, F. Alberto; Vinet, Luc; Zhedanov, Alexei
2013
An urn model associated with Jacobi polynomials. Zbl 1188.60040
Grünbaum, F. Alberto
2010
The noncommutative bispectral problem for operators of order one. Zbl 1157.39001
Castro, Mirta M.; Grünbaum, F. Alberto
2008
P. A. M. Dirac meets M. G. Krein: matrix orthogonal polynomials and Dirac’s equation. Zbl 1094.33011
Durán, Antonio J.; Grünbaum, F. Alberto
2006
The Wilson bispectral involution: Some elementary examples. Zbl 0924.34074
Grünbaum, F. Alberto; Haine, Luc
1999
Some new explorations into the mystery of time and band limiting. Zbl 0778.05084
Grünbaum, F. Alberto
1992
Diffuse tomography: Computational aspects of the isotropic case. Zbl 0760.65110
Grünbaum, F. Alberto; Zubelli, Jorge P.
1992
On sets of differences. Zbl 0377.60025
Grünbaum, F. Alberto
1977
On the existence of a ”wave operator” for the Boltzmann equation. Zbl 0254.45018
Grünbaum, F. Alberto
1972
Stochastic Darboux transformations for quasi-birth-and-death processes and urn models. Zbl 07096794
Grünbaum, F. Alberto; de la Iglesia, Manuel D.
2019
The quantum walk of F. Riesz. Zbl 1316.81010
Grünbaum, F. Alberto; Velázquez, Luis
2013
On a seminal paper by Karlin and McGregor. Zbl 1383.60064
Castro, Mirta M.; Grünbaum, F. Alberto
2013
Block tridiagonal matrices and a beefed-up version of the Ehrenfest urn model. Zbl 1178.33008
Grünbaum, F. Alberto
2009
The Rahman polynomials are bispectral. Zbl 1193.33027
Grünbaum, F. Alberto
2007
Diffuse tomography as a source of challenging nonlinear inverse problems for a general class of networks. Zbl 1062.92043
Grünbaum, F. Alberto
2004
Linear operator pencils on Lie algebras and Laurent biorthogonal polynomials. Zbl 1071.33013
Grünbaum, F. A.; Vinet, Luc; Zhedanov, Alexei
2004
Explicit inversion formulas for a model in diffuse tomography. Zbl 1016.92021
Grünbaum, F. Alberto; Matusevich, Laura Felicia
2002
Discrete models of the harmonic oscillator and a discrete analogue of Gauss’ hypergeometric equation. Zbl 1003.33003
Grünbaum, F. Alberto
2001
Bispectrality and time-band limiting: matrix-valued polynomials. Zbl 07236276
Grünbaum, F. Alberto; Pacharoni, Inés; Zurrián, Ignacio
2020
Stochastic Darboux transformations for quasi-birth-and-death processes and urn models. Zbl 07096794
Grünbaum, F. Alberto; de la Iglesia, Manuel D.
2019
Algebraic Heun operator and band-time limiting. Zbl 1405.33025
Grünbaum, F. Alberto; Vinet, Luc; Zhedanov, Alexei
2018
The topological classification of one-dimensional symmetric quantum walks. Zbl 1391.82027
Cedzich, C.; Geib, T.; Grünbaum, F. A.; Stahl, C.; Velázquez, L.; Werner, A. H.; Werner, R. F.
2018
A further look at time-and-band limiting for matrix orthogonal polynomials. Zbl 1411.33008
Castro, M.; Grünbaum, F. A.; Pacharoni, I.; Zurrián, I.
2018
Stochastic LU factorizations, Darboux transformations and urn models. Zbl 1402.60090
Grünbaum, F. Alberto; de la Iglesia, Manuel D.
2018
Some limit laws for quantum walks with applications to a version of the Parrondo paradox. Zbl 1398.81061
Machida, Takuya; Grünbaum, F. Alberto
2018
A generalization of Schur functions: applications to Nevanlinna functions, orthogonal polynomials, random walks and unitary and open quantum walks. Zbl 06833446
Grünbaum, F. A.; Velázquez, L.
2018
Tridiagonalization and the Heun equation. Zbl 1364.34126
Grünbaum, F. Alberto; Vinet, Luc; Zhedanov, Alexei
2017
Time and band limiting for matrix valued functions: an integral and a commuting differential operator. Zbl 1367.47078
Grünbaum, F. A.; Pacharoni, I.; Zurrián, I.
2017
Time-and-band limiting for matrix orthogonal polynomials of Jacobi type. Zbl 1376.33010
Castro, M.; Grünbaum, F. A.
2017
Bulk-edge correspondence of one-dimensional quantum walks. Zbl 1342.82064
Cedzich, C.; Grünbaum, F. A.; Stahl, C.; Velázquez, L.; Werner, A. H.; Werner, R. F.
2016
A quantum dynamical approach to matrix Khrushchev’s formulas. Zbl 1371.30004
Cedzich, C.; Grünbaum, F. A.; Velázquez, L.; Werner, A. H.; Werner, R. F.
2016
Maximal Parrondo’s paradox for classical and quantum Markov chains. Zbl 1333.60158
Grünbaum, F. Alberto; Pejic, Michael
2016
The Darboux process and time-and-band limiting for matrix orthogonal polynomials. Zbl 1326.33013
Castro, M.; Grünbaum, F. A.
2015
Time and band limiting for matrix valued functions, an example. Zbl 1318.33018
Grünbaum, F. Alberto; Pacharoni, Inés; Zurrián, Ignacio Nahuel
2015
Quantum recurrence of a subspace and operator-valued Schur functions. Zbl 1296.37014
Bourgain, J.; Grünbaum, F. A.; Velázquez, L.; Wilkening, J.
2014
Some noncommutative matrix algebras arising in the bispectral problem. Zbl 1353.34104
Grünbaum, F. Alberto
2014
Recurrence for discrete time unitary evolutions. Zbl 1276.81087
Grünbaum, F. A.; Velázquez, L.; Werner, A. H.; Werner, R. F.
2013
Two stochastic models of a random walk in the $$\mathrm U(n)$$-spherical duals of $$U(n+1)$$. Zbl 1279.60010
Grünbaum, F. A.; Pacharoni, I.; Tirao, J.
2013
Birth and death processes and quantum spin chains. Zbl 1285.82028
Grünbaum, F. Alberto; Vinet, Luc; Zhedanov, Alexei
2013
The quantum walk of F. Riesz. Zbl 1316.81010
Grünbaum, F. Alberto; Velázquez, Luis
2013
On a seminal paper by Karlin and McGregor. Zbl 1383.60064
Castro, Mirta M.; Grünbaum, F. Alberto
2013
The CGMV method for quantum walks. Zbl 1252.82082
Cantero, M. J.; Grünbaum, F. A.; Moral, L.; Velázquez, L.
2012
One-dimensional quantum walks with one defect. Zbl 1251.81026
Cantero, M. J.; Grünbaum, F. A.; Moral, L.; Velázquez, L.
2012
The Darboux process and a noncommutative bispectral problem: some explorations and challenges. Zbl 1263.34022
Grünbaum, F. Alberto
2011
A system of multivariable Krawtchouk polynomials and a probabilistic application. Zbl 1244.33003
Grünbaum, F. Alberto; Rahman, Mizan
2011
Properties of matrix orthogonal polynomials via their Riemann-Hilbert characterization. Zbl 1242.42020
Grünbaum, F. Alberto; De La Iglesia, Manuel D.; Martínez-Finkelshtein, Andrei
2011
Matrix-valued Szegő polynomials and quantum random walks. Zbl 1186.81036
Cantero, M. J.; Moral, L.; Grünbaum, F. Alberto; Velázquez, L.
2010
On a family of 2-variable orthogonal Krawtchouk polynomials. Zbl 1220.33008
Grünbaum, F. Alberto; Rahman, Mizan
2010
An urn model associated with Jacobi polynomials. Zbl 1188.60040
Grünbaum, F. Alberto
2010
The Karlin-McGregor formula for a variant of a discrete version of Walsh’s spider. Zbl 1187.37094
Grünbaum, F. Alberto
2009
Matrix differential equations and scalar polynomials satisfying higher order recursions. Zbl 1163.42009
Durán, Antonio J.; Grünbaum, F. Alberto
2009
Block tridiagonal matrices and a beefed-up version of the Ehrenfest urn model. Zbl 1178.33008
Grünbaum, F. Alberto
2009
Matrix valued orthogonal polynomials arising from group representation theory and a family of quasi-birth-and-death processes. Zbl 1163.60033
Grünbaum, F. Alberto; de la Iglesia, Manuel D.
2008
Random walks and orthogonal polynomials: some challenges. Zbl 1184.33004
Grünbaum, F. Alberto
2008
The noncommutative bispectral problem for operators of order one. Zbl 1157.39001
Castro, Mirta M.; Grünbaum, F. Alberto
2008
The algebra of differential operators associated to a weight matrix. Zbl 1120.33008
Grünbaum, F. Alberto; Tirao, Juan
2007
Matrix orthogonal polynomials satisfying second-order differential equations: coping without help from group representation theory. Zbl 1221.42046
Durán, Antonio J.; Grünbaum, F. Alberto
2007
Matrix-valued orthogonal polynomials related to $$\mathrm{SU}(N+1)$$, their algebras of differential operators, and the corresponding curves. Zbl 1149.33002
Grünbaum, F. Alberto; de la Iglesia, Manuel D.
2007
The Rahman polynomials are bispectral. Zbl 1193.33027
Grünbaum, F. Alberto
2007
The algebra of differential operators associated to a family of matrix-valued orthogonal polynomials: five instructive examples. Zbl 1130.33004
Castro, Mirta M.; Grünbaum, F. Alberto
2006
P. A. M. Dirac meets M. G. Krein: matrix orthogonal polynomials and Dirac’s equation. Zbl 1094.33011
Durán, Antonio J.; Grünbaum, F. Alberto
2006
Structural formulas for orthogonal matrix polynomials satisfying second-order differential equations. I. Zbl 1097.42018
Durán, Antonio J.; Grünbaum, F. Alberto
2005
Matrix valued orthogonal polynomials of Jacobi type: the role of group representation theory. Zbl 1082.33006
Grünbaum, F. Alberto; Pacharoni, Inés; Tirao, Juan Alfredo
2005
A survey on orthogonal matrix polynomials satisfying second order differential equations. Zbl 1060.42017
Durán, Antonio J.; Grünbaum, F. Alberto
2005
Orthogonal matrix polynomials, scalar-type Rodrigues formulas and Pearson equations. Zbl 1066.42018
Durán, Antonio J.; Grünbaum, F. Alberto
2005
Orthogonal matrix polynomials satisfying first order differential equations: a collection of instructive examples. Zbl 1100.42015
Castro, Mirta M.; Grünbaum, F. Alberto
2005
A characterization for a class of weight matrices with orthogonal matrix polynomials satisfying second-order differential equations. Zbl 1102.42013
Durán, Antonio J.; Grünbaum, F. Alberto
2005
Orthogonal matrix polynomials satisfying second-order differential equations. Zbl 1073.33009
Durán, Antonio J.; Grünbaum, F. Alberto
2004
An invitation to matrix-valued spherical functions: Linearization of products in the case of complex projective space $$P_2(\mathbb C)$$. Zbl 1075.33004
Grünbaum, F. Alberto; Pacharoni, Inés; Tirao, Juan
2004
The prolate spheroidal phenomenon as a consequence of bispectrality. Zbl 1085.47056
Grünbaum, F. Alberto; Yakimov, Milen
2004
Diffuse tomography as a source of challenging nonlinear inverse problems for a general class of networks. Zbl 1062.92043
Grünbaum, F. Alberto
2004
Linear operator pencils on Lie algebras and Laurent biorthogonal polynomials. Zbl 1071.33013
Grünbaum, F. A.; Vinet, Luc; Zhedanov, Alexei
2004
Matrix valued orthogonal polynomials of the Jacobi type. Zbl 1070.33011
Grünbaum, F. A.; Pacharoni, I.; Tirao, J.
2003
Matrix valued Jacobi polynomials. Zbl 1026.33008
Grünbaum, F. Alberto
2003
A noncommutative version of the bispectral problem. Zbl 1038.39012
Grünbaum, F. Alberto; Iliev, Plamen
2003
The Heisenberg inequality for the discrete Fourier transform. Zbl 1053.42009
Grünbaum, F. Alberto
2003
Matrix valued spherical functions associated to the complex projective plane. Zbl 0996.43013
Grünbaum, F. A.; Pacharoni, I.; Tirao, J.
2002
Discrete bispectral Darboux transformations from Jacobi operators. Zbl 1051.39020
Grünbaum, F. Alberto; Yakimov, Milen
2002
Heat kernel expansions on the integers. Zbl 0996.35077
Grünbaum, F. Alberto; Iliev, Plamen
2002
Matrix valued spherical functions associated to the three dimensional hyperbolic space. Zbl 1048.22005
Grünbaum, F. A.; Pacharoni, I.; Tirao, J.
2002
Explicit inversion formulas for a model in diffuse tomography. Zbl 1016.92021
Grünbaum, F. Alberto; Matusevich, Laura Felicia
2002
A matrix-valued solution to Bochner’s problem. Zbl 0990.22012
Grünbaum, F. A.; Pacharoni, I.; Tirao, J.
2001
The bispectral problem: An overview. Zbl 0999.47018
Grünbaum, F. Alberto
2001
Electrostatic interpretation for the zeros of certain polynomials and the Darboux process. Zbl 0989.42006
Grünbaum, F. Alberto
2001
Special issue to celebrate Pierre Sabatier’s 65th birthday. Papers from the conference “RCP264: Inverse problems and nonlinearity—theory and applications”, Montpellier, France, June 20–24, 2000. Zbl 0988.00112
Bertero, Mario (ed.); Caputo, Jean Guy (ed.); Grünbaum, F. Alberto (ed.); Natterer, Frank (ed.)
2001
Discrete models of the harmonic oscillator and a discrete analogue of Gauss’ hypergeometric equation. Zbl 1003.33003
Grünbaum, F. Alberto
2001
A nonlinear inverse problem inspired by three-dimensional diffuse tomography. Zbl 1003.65146
Grünbaum, F. Alberto
2001
Some functions that generalize the Krall-Laguerre polynomials. Zbl 0926.33007
Grünbaum, F. Alberto; Haine, Luc; Horozov, Emil
1999
On a $$q$$-analogue of the string equation and a generalization of the classical orthogonal polynomials. Zbl 0938.33010
Grünbaum, F. Alberto; Haine, Luc
1999
The Wilson bispectral involution: Some elementary examples. Zbl 0924.34074
Grünbaum, F. Alberto; Haine, Luc
1999
Associated polynomials, spectral matrices and the bispectral problem. Zbl 0956.33007
Grünbaum, F. Alberto; Haine, Luc
1999
Variations on a theme of Heine and Stieltjes: An electrostatic interpretation of the zeros of certain polynomials. Zbl 0934.33012
Grünbaum, F. Alberto
1998
Some bispectral musings. Zbl 0944.34062
Grünbaum, F. Alberto
1998
Bispectral Darboux transformations: an extension of the Krall polynomials. Zbl 1125.37321
Grünbaum, F. Alberto; Haine, Luc
1997
A theorem of Bochner, revisited. Zbl 0868.35116
Grünbaum, F. Alberto; Haine, Luc
1997
Some functions that generalize the Askey-Wilson polynomials. Zbl 0871.33009
Grünbaum, F. Alberto; Haine, Luc
1997
On the Krall-Hermite and the Krall-Bessel polynomials. Zbl 0910.33004
Grünbaum, F. Alberto; Haine, Luc; Horozov, Emil
1997
On a $$q$$-analogue of Gauss equation and some $$q$$-Riccati equations. Zbl 0870.39003
Grünbaum, F. Alberto; Haine, Luc
1997
How many parameters can one solve for in diffuse tomography? Zbl 0880.60105
Grünbaum, F. A.; Patch, S. K.
1997
Orthogonal polynomials satisfying differential equations: The role of the Darboux transformation. Zbl 0865.33008
Grünbaum, F. Alberto; Haine, Luc
1996
The $$q$$-version of a theorem of Bochner. Zbl 0865.33012
Grünbaum, F. Alberto; Haine, Luc
1996
Band-time-band limiting integral operators and commuting differential operators. Zbl 0878.47031
Grünbaum, F. Alberto
1996
The use of higher-order invariants in the determination of generalized Patterson cyclotomic sets. Zbl 1176.82034
Grünbaum, F. Alberto; Moore, Calvin C.
1995
Time-band limiting and the bispectral problem. Zbl 0802.34086
Grünbaum, F. Alberto
1994
The use of Graßmann identities for inversion of a general model in diffuse tomography. Zbl 0795.92015
Grünbaum, F. Alberto; Patch, S. K.
1993
Diffuse tomography: The isotropic case. Zbl 0760.65109
Grünbaum, F. Alberto
1992
Some new explorations into the mystery of time and band limiting. Zbl 0778.05084
Grünbaum, F. Alberto
1992
Diffuse tomography: Computational aspects of the isotropic case. Zbl 0760.65110
Grünbaum, F. Alberto; Zubelli, Jorge P.
1992
An inverse problem in transport theory: Diffuse tomography. Zbl 0789.60063
Grünbaum, F. Alberto
1992
Radar and sonar. Part II. Proceedings of the lectures given during the 2nd week of the IMA summer program ’Radar and sonar’, June 18-June 29, 1990, in Minneapolis, MN (USA). Zbl 0741.00059
Grünbaum, F. Alberto (ed.); Bernfeld, Marvin (ed.); Blahut, Richard E. (ed.)
1992
Trying to beat Heisenberg. Zbl 0702.35199
Grünbaum, F. Alberto
1990
Darboux’s method and some “rank two” explicit solutions of the KP equation. Zbl 0722.35080
Grünbaum, F. A.
1990
Concentrating a potential and its scattering transform for a discrete version of the Schrödinger and Zakharov-Shabat operators. Zbl 0703.58053
Grünbaum, F. Alberto
1990
Signal processing. Part II: Control theory and applications. Based on lectures held at the IMA, Minneapolis, MN (USA) from June 27 to August 5, 1988. Zbl 0691.00018
Auslander, L. (ed.); Grünbaum, F. A. (ed.); Helton, J. W. (ed.); Kailath, T. (ed.); Khargoneka, P. (ed.); Mitter, S. (ed.)
1990
The Fourier transform and the discrete Fourier transform. Zbl 0674.65114
Auslander, Louis; Grünbaum, F. Alberto
1989
The scattering problem for a phase-modulated hyperbolic secant pulse. Zbl 0698.35113
Grünbaum, F. Alberto
1989
Commuting pairs of linear ordinary differential operators of orders four and six. Zbl 0654.47027
Grünbaum, F. Alberto
1988
Differential equations in the spectral parameter. Zbl 0625.34007
Duistermaat, J. J.; Grünbaum, F. A.
1986
...and 33 more Documents
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#### Cited by 673 Authors

 52 Grünbaum, Francisco Alberto 32 Duran, Antonio J. 19 Iliev, Plamen 19 Marcellán Español, Francisco 17 Vinet, Luc 15 Domínguez de la Iglesia, Manuel 15 Zhedanov, Alexei S. 12 Terwilliger, Paul M. 12 Velázquez, Luis 11 Fillman, Jake 10 Horozov, Emil Ivanov 10 Koelink, Erik 10 Konno, Norio 9 Ismail, Mourad El-Houssieny 9 Pacharoni, Inés 9 Segawa, Etsuo 8 Milson, Robert 8 Román, Pablo Manuel 8 Tirao, Juan 8 van Diejen, Jan Felipe 8 Zubelli, Jorge P. 7 Damanik, David 7 Emsiz, Erdal 7 Joye, Alain 7 Kasman, Alex 6 Álvarez-Nodarse, Renato 6 Baseilhac, Pascal 6 Cantero, María José 6 Dette, Holger 6 Garza, Luis E. 6 Georgieva, Irina 6 Gómez-Ullate, David 6 Haine, Luc 6 Ishkin, Khabir Kabirovich 6 Mischler, Stéphane 6 Moral, Leandro 6 Ong, Darren C. 6 Suzuki, Akito 6 Werner, Albert H. 5 Cedzich, Christopher 5 Ciaurri, Óscar 5 Dueñas, Herbert 5 Lardizabal, Carlos F. 5 Mañas, Manuel 5 Previato, Emma 5 Roncal, Luz 5 Veselov, Alexander Petrovich 5 Werner, Reinhard F. 5 Zurrián, Ignacio Nahuel 4 Alfaro García, Manuel 4 Alzer, Horst 4 Bourget, Alain 4 Carlen, Eric Anders 4 Castro, Mirta M. 4 Chalykh, Oleg A. 4 Choque Rivero, Abdon Eddy 4 Crampé, Nicolas 4 De Los Ríos, Ana M. 4 Geib, T. 4 Hofreither, Clemens 4 Ito, Tatsuro 4 Kwon, Kil Hyun 4 Rezola, María Luisa 4 Sakhnovich, Alexander L. 4 Tsujimoto, Satoshi 4 Varona Malumbres, Juan Luis 3 Alhaidari, Abdulaziz D. 3 Asch, Joachim 3 Atakishiev, Natig M. 3 Berest, Yuri Yu. 3 Bergeron, Geoffroy 3 Bueno, María Isabel 3 Durak-Ata, Lutfiye 3 Fehér, László Gy. 3 Fernández, Lidia 3 Fuentes, Edinson 3 García-Ardila, Juan Carlos 3 Grandati, Yves 3 Griffiths, Robert C. 3 Huertas Cejudo, Edmundo José 3 Karoui, Abderrazek 3 Kuijlaars, Arno B. J. 3 Lederman, Roy R. 3 Littlejohn, Lance L. 3 Magnus, Alphonse Ph. 3 Martínez-Finkelshtein, Andrei 3 Mironov, Andreĭ Evgen’evich 3 Mouhot, Clément 3 Odake, Satoru 3 Peña, Ana 3 Qu, Gangrong 3 Rafaeli, Fernando Rodrigo 3 Rokhlin, Vladimir 3 Ronveaux, André 3 Sato, Iwao 3 Serbes, Ahmet 3 Tirao, Juan Alfredo 3 Trench, William F. 3 Yakimov, Milen T. 3 Zheglov, Alexander B. ...and 573 more Authors
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#### Cited in 173 Serials

 41 Journal of Mathematical Analysis and Applications 41 Journal of Approximation Theory 32 Journal of Computational and Applied Mathematics 26 Journal of Mathematical Physics 22 Communications in Mathematical Physics 22 Linear Algebra and its Applications 18 Proceedings of the American Mathematical Society 18 Quantum Information Processing 13 Letters in Mathematical Physics 12 Journal of Statistical Physics 11 Integral Transforms and Special Functions 10 Advances in Mathematics 8 Transactions of the American Mathematical Society 8 Physica D 8 Constructive Approximation 8 Applied and Computational Harmonic Analysis 8 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 7 Numerical Functional Analysis and Optimization 7 Advances in Applied Mathematics 7 The Journal of Fourier Analysis and Applications 6 Reviews in Mathematical Physics 6 Journal of Functional Analysis 6 The Ramanujan Journal 6 Annales Henri Poincaré 5 Physics Letters. A 5 Annales de l’Institut Fourier 5 Bulletin des Sciences Mathématiques 5 Journal of High Energy Physics 5 Journal of Physics A: Mathematical and Theoretical 4 Inverse Problems 4 Integral Equations and Operator Theory 4 Journal of Differential Equations 4 SIAM Journal on Algebraic and Discrete Methods 4 Applied Mathematics Letters 4 Mathematical Physics, Analysis and Geometry 3 Archive for Rational Mechanics and Analysis 3 Communications on Pure and Applied Mathematics 3 Linear and Multilinear Algebra 3 Mathematical Notes 3 Theoretical and Mathematical Physics 3 Annali di Matematica Pura ed Applicata. Serie Quarta 3 Applied Mathematics and Computation 3 Inventiones Mathematicae 3 Journal of Multivariate Analysis 3 Numerische Mathematik 3 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 3 Acta Applicandae Mathematicae 3 Probability Theory and Related Fields 3 International Journal of Mathematics 3 The Annals of Applied Probability 3 Journal de Mathématiques Pures et Appliquées. Neuvième Série 3 Stochastic Processes and their Applications 3 Indagationes Mathematicae. New Series 3 Journal of Mathematical Sciences (New York) 3 Doklady Mathematics 3 Journal of Nonlinear Mathematical Physics 3 Journal of Statistical Mechanics: Theory and Experiment 3 Inverse Problems and Imaging 3 Analysis and Mathematical Physics 3 Quantum Studies: Mathematics and Foundations 2 Applicable Analysis 2 Journal d’Analyse Mathématique 2 Journal of Computational Physics 2 Nuclear Physics. B 2 Reports on Mathematical Physics 2 Rocky Mountain Journal of Mathematics 2 The Annals of Probability 2 Compositio Mathematica 2 Duke Mathematical Journal 2 Functional Analysis and its Applications 2 Journal of Algebra 2 Journal of Applied Probability 2 Journal of Number Theory 2 Results in Mathematics 2 SIAM Journal on Numerical Analysis 2 Siberian Mathematical Journal 2 Studies in Applied Mathematics 2 Acta Mathematicae Applicatae Sinica. English Series 2 Signal Processing 2 SIAM Journal on Mathematical Analysis 2 SIAM Journal on Scientific Computing 2 Discrete and Continuous Dynamical Systems 2 Mathematical Problems in Engineering 2 Transformation Groups 2 Bulletin of the Brazilian Mathematical Society. New Series 2 Journal of Algebra and its Applications 2 Mediterranean Journal of Mathematics 2 Bulletin of the American Mathematical Society 2 Complex Analysis and Operator Theory 2 Mathematical Sciences 1 Analysis Mathematica 1 Archive for History of Exact Sciences 1 Bulletin of the Australian Mathematical Society 1 Computers & Mathematics with Applications 1 Israel Journal of Mathematics 1 Journal of Fluid Mechanics 1 Journal of the Franklin Institute 1 Mathematical Methods in the Applied Sciences 1 Physica A 1 Russian Mathematical Surveys ...and 73 more Serials
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#### Cited in 52 Fields

 224 Special functions (33-XX) 151 Harmonic analysis on Euclidean spaces (42-XX) 102 Quantum theory (81-XX) 100 Operator theory (47-XX) 89 Probability theory and stochastic processes (60-XX) 83 Ordinary differential equations (34-XX) 77 Partial differential equations (35-XX) 73 Statistical mechanics, structure of matter (82-XX) 63 Numerical analysis (65-XX) 57 Dynamical systems and ergodic theory (37-XX) 54 Linear and multilinear algebra; matrix theory (15-XX) 46 Difference and functional equations (39-XX) 32 Combinatorics (05-XX) 24 Nonassociative rings and algebras (17-XX) 23 Integral transforms, operational calculus (44-XX) 23 Information and communication theory, circuits (94-XX) 19 Topological groups, Lie groups (22-XX) 18 Functions of a complex variable (30-XX) 18 Approximations and expansions (41-XX) 17 Integral equations (45-XX) 16 Functional analysis (46-XX) 16 Optics, electromagnetic theory (78-XX) 14 Algebraic geometry (14-XX) 14 Real functions (26-XX) 12 Biology and other natural sciences (92-XX) 11 Abstract harmonic analysis (43-XX) 11 Global analysis, analysis on manifolds (58-XX) 10 Differential geometry (53-XX) 9 Associative rings and algebras (16-XX) 8 Commutative algebra (13-XX) 8 Fluid mechanics (76-XX) 7 Computer science (68-XX) 7 Mechanics of particles and systems (70-XX) 6 Number theory (11-XX) 6 Statistics (62-XX) 4 Group theory and generalizations (20-XX) 4 General topology (54-XX) 4 Relativity and gravitational theory (83-XX) 4 Systems theory; control (93-XX) 3 Potential theory (31-XX) 2 General and overarching topics; collections (00-XX) 2 History and biography (01-XX) 2 Measure and integration (28-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Operations research, mathematical programming (90-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Mathematical logic and foundations (03-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Convex and discrete geometry (52-XX) 1 Algebraic topology (55-XX) 1 Astronomy and astrophysics (85-XX) 1 Geophysics (86-XX)