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Grünbaum, Francisco Alberto

Author ID: grunbaum.francisco-alberto Recent zbMATH articles by "Grünbaum, Francisco Alberto"
Published as: Grünbaum, F. Alberto; Grünbaum, F. A.; Gruenbaum, F. Alberto; Grünbaum, Francisco Alberto; Grünbaum, F.; Gruenbaum, F. A.
Homepage: https://math.berkeley.edu/people/faculty/f-alberto-gruenbaum
External Links: MGP · GND
all top 5

Serials

14 Inverse Problems
8 IMRN. International Mathematics Research Notices
7 Communications in Mathematical Physics
7 Journal of Computational and Applied Mathematics
7 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications
6 Journal of Mathematical Analysis and Applications
5 Communications on Pure and Applied Mathematics
4 Proceedings of the American Mathematical Society
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 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 Applied and Computational Harmonic Analysis
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 L’Enseignement Mathématique. 2e Série
1 Indagationes Mathematicae. New Series
1 Experimental Mathematics
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 Nieuw Archief voor Wiskunde. Vijfde Serie
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
1 Contemporary Mathematicians
all top 5

Fields

64 Special functions (33-XX)
43 Probability theory and stochastic processes (60-XX)
40 Harmonic analysis on Euclidean spaces (42-XX)
28 Operator theory (47-XX)
27 Ordinary differential equations (34-XX)
24 Partial differential equations (35-XX)
22 Numerical analysis (65-XX)
19 Topological groups, Lie groups (22-XX)
18 Biology and other natural sciences (92-XX)
17 Quantum theory (81-XX)
16 Linear and multilinear algebra; matrix theory (15-XX)
14 Difference and functional equations (39-XX)
13 Integral transforms, operational calculus (44-XX)
12 Dynamical systems and ergodic theory (37-XX)
11 Statistical mechanics, structure of matter (82-XX)
8 Information and communication theory, circuits (94-XX)
7 Integral equations (45-XX)
5 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 Associative rings and algebras (16-XX)
3 Nonassociative rings and algebras (17-XX)
3 Functions of a complex variable (30-XX)
3 Statistics (62-XX)
3 Optics, electromagnetic theory (78-XX)
2 History and biography (01-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 Approximations and expansions (41-XX)
1 Computer science (68-XX)

Publications by Year

Citations contained in zbMATH Open

140 Publications have been cited 1,813 times in 833 Documents Cited by Year
Differential equations in the spectral parameter. Zbl 0625.34007
Duistermaat, J. J.; Grünbaum, F. A.
176
1986
Matrix-valued Szegő polynomials and quantum random walks. Zbl 1186.81036
Cantero, M. J.; Moral, L.; Grünbaum, F. Alberto; Velázquez, L.
56
2010
Some functions that generalize the Krall-Laguerre polynomials. Zbl 0926.33007
Grünbaum, F. Alberto; Haine, Luc; Horozov, Emil
53
1999
Matrix valued spherical functions associated to the complex projective plane. Zbl 0996.43013
Grünbaum, F. A.; Pacharoni, I.; Tirao, J.
52
2002
Bispectral Darboux transformations: an extension of the Krall polynomials. Zbl 1125.37321
Grünbaum, F. Alberto; Haine, Luc
52
1997
Orthogonal matrix polynomials satisfying second-order differential equations. Zbl 1073.33009
Durán, Antonio J.; Grünbaum, F. Alberto
48
2004
Orthogonal polynomials satisfying differential equations: The role of the Darboux transformation. Zbl 0865.33008
Grünbaum, F. Alberto; Haine, Luc
47
1996
Matrix valued orthogonal polynomials of the Jacobi type. Zbl 1070.33011
Grünbaum, F. A.; Pacharoni, I.; Tirao, J.
38
2003
Discrete bispectral Darboux transformations from Jacobi operators. Zbl 1051.39020
Grünbaum, F. Alberto; Yakimov, Milen
38
2002
Recurrence for discrete time unitary evolutions. Zbl 1276.81087
Grünbaum, F. A.; Velázquez, L.; Werner, A. H.; Werner, R. F.
37
2013
The \(q\)-version of a theorem of Bochner. Zbl 0865.33012
Grünbaum, F. Alberto; Haine, Luc
36
1996
The CGMV method for quantum walks. Zbl 1252.82082
Cantero, M. J.; Grünbaum, F. A.; Moral, L.; Velázquez, L.
36
2012
Matrix valued Jacobi polynomials. Zbl 1026.33008
Grünbaum, F. Alberto
34
2003
Algebraic Heun operator and band-time limiting. Zbl 1405.33025
Grünbaum, F. Alberto; Vinet, Luc; Zhedanov, Alexei
34
2018
Variations on a theme of Heine and Stieltjes: An electrostatic interpretation of the zeros of certain polynomials. Zbl 0934.33012
Grünbaum, F. Alberto
33
1998
Structural formulas for orthogonal matrix polynomials satisfying second-order differential equations. I. Zbl 1097.42018
Durán, Antonio J.; Grünbaum, F. Alberto
31
2005
One-dimensional quantum walks with one defect. Zbl 1251.81026
Cantero, M. J.; Grünbaum, F. A.; Moral, L.; Velázquez, L.
30
2012
Propagation of chaos for the Boltzmann equation. Zbl 0236.45011
Grünbaum, F. Alberto
29
1971
Differential operators commuting with finite convolution integral operators: Some non-Abelian examples. Zbl 0497.22012
Gruenbaum, F. A.; Longhi, L.; Perlstadt, M.
28
1982
Eigenvectors of a Toeplitz matrix: Discrete version of the prolate spheroidal wave functions. Zbl 0519.47019
Gruenbaum, F. Alberto
28
1981
The algebra of differential operators associated to a weight matrix. Zbl 1120.33008
Grünbaum, F. Alberto; Tirao, Juan
27
2007
Quantum recurrence of a subspace and operator-valued Schur functions. Zbl 1296.37014
Bourgain, J.; Grünbaum, F. A.; Velázquez, L.; Wilkening, J.
26
2014
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.
25
2018
Tridiagonalization and the Heun equation. Zbl 1364.34126
Grünbaum, F. Alberto; Vinet, Luc; Zhedanov, Alexei
25
2017
The bispectral problem: An overview. Zbl 0999.47018
Grünbaum, F. Alberto
24
2001
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.
23
2016
Matrix valued orthogonal polynomials of Jacobi type: the role of group representation theory. Zbl 1082.33006
Grünbaum, F. Alberto; Pacharoni, Inés; Tirao, Juan Alfredo
22
2005
A survey on orthogonal matrix polynomials satisfying second order differential equations. Zbl 1060.42017
Durán, Antonio J.; Grünbaum, F. Alberto
22
2005
A matrix-valued solution to Bochner’s problem. Zbl 0990.22012
Grünbaum, F. A.; Pacharoni, I.; Tirao, J.
19
2001
Toeplitz matrices commuting with tridiagonal matrices. Zbl 0477.15005
Gruenbaum, F. Alberto
19
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
18
2006
The eigenvectors of the discrete Fourier transform: A version of the Hermite functions. Zbl 0516.65099
Gruenbaum, F. Alberto
18
1982
Tomographic reconstruction with arbitrary directions. Zbl 0441.93031
Davison, M. E.; Grünbaum, F. Alberto
18
1981
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.
17
2008
Orthogonal matrix polynomials, scalar-type Rodrigues formulas and Pearson equations. Zbl 1066.42018
Durán, Antonio J.; Grünbaum, F. Alberto
17
2005
Orthogonal matrix polynomials satisfying first order differential equations: a collection of instructive examples. Zbl 1100.42015
Castro, Mirta M.; Grünbaum, F. Alberto
17
2005
A new property of reproducing kernels for classical orthogonal polynomials. Zbl 0562.33008
Grünbaum, F. Alberto
16
1983
Time-band limiting and the bispectral problem. Zbl 0802.34086
Grünbaum, F. Alberto
16
1994
Random walks and orthogonal polynomials: some challenges. Zbl 1184.33004
Grünbaum, F. Alberto
16
2008
A theorem of Bochner, revisited. Zbl 0868.35116
Grünbaum, F. Alberto; Haine, Luc
15
1997
Properties of matrix orthogonal polynomials via their Riemann-Hilbert characterization. Zbl 1242.42020
Grünbaum, F. Alberto; De La Iglesia, Manuel D.; Martínez-Finkelshtein, Andrei
15
2011
Commuting pairs of linear ordinary differential operators of orders four and six. Zbl 0654.47027
Grünbaum, F. Alberto
14
1988
The Darboux process and a noncommutative bispectral problem: some explorations and challenges. Zbl 1263.34022
Grünbaum, F. Alberto
13
2011
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
13
2005
A study of Fourier space methods for ”limited angle” image reconstruction. Zbl 0458.65105
Grünbaum, F. Alberto
13
1980
Some bispectral musings. Zbl 0944.34062
Grünbaum, F. Alberto
12
1998
Matrix orthogonal polynomials satisfying second-order differential equations: coping without help from group representation theory. Zbl 1221.42046
Durán, Antonio J.; Grünbaum, F. Alberto
12
2007
Heat kernel expansions on the integers. Zbl 0996.35077
Grünbaum, F. Alberto; Iliev, Plamen
12
2002
Some functions that generalize the Askey-Wilson polynomials. Zbl 0871.33009
Grünbaum, F. Alberto; Haine, Luc
11
1997
A system of multivariable Krawtchouk polynomials and a probabilistic application. Zbl 1244.33003
Grünbaum, F. Alberto; Rahman, Mizan
11
2011
Commuting differential operators for the finite Laplace transform. Zbl 0603.44002
Bertero, M.; Grünbaum, F. A.
10
1985
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
9
2001
Electrostatic interpretation for the zeros of certain polynomials and the Darboux process. Zbl 0989.42006
Grünbaum, F. Alberto
9
2001
Linearization for the Boltzmann equation. Zbl 0236.45012
Grünbaum, F. Alberto
9
1972
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
9
2004
A generalization of Schur functions: applications to Nevanlinna functions, orthogonal polynomials, random walks and unitary and open quantum walks. Zbl 1464.47011
Grünbaum, F. A.; Velázquez, L.
9
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.
9
2017
Matrix valued spherical functions associated to the three dimensional hyperbolic space. Zbl 1048.22005
Grünbaum, F. A.; Pacharoni, I.; Tirao, J.
9
2002
The use of higher-order invariants in the determination of generalized Patterson cyclotomic sets. Zbl 1176.82034
Grünbaum, F. Alberto; Moore, Calvin C.
8
1995
On the Krall-Hermite and the Krall-Bessel polynomials. Zbl 0910.33004
Grünbaum, F. Alberto; Haine, Luc; Horozov, Emil
8
1997
A noncommutative version of the bispectral problem. Zbl 1038.39012
Grünbaum, F. Alberto; Iliev, Plamen
8
2003
The Karlin-McGregor formula for a variant of a discrete version of Walsh’s spider. Zbl 1187.37094
Grünbaum, F. Alberto
8
2009
The Darboux process and time-and-band limiting for matrix orthogonal polynomials. Zbl 1326.33013
Castro, M.; Grünbaum, F. A.
8
2015
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.
8
2016
Stochastic LU factorizations, Darboux transformations and urn models. Zbl 1402.60090
Grünbaum, F. Alberto; de la Iglesia, Manuel D.
8
2018
Differential operators commuting with convolution integral operators. Zbl 0506.45018
Grünbaum, F. Alberto
7
1983
On a \(q\)-analogue of the string equation and a generalization of the classical orthogonal polynomials. Zbl 0938.33010
Grünbaum, F. Alberto; Haine, Luc
7
1999
Band-time-band limiting integral operators and commuting differential operators. Zbl 0878.47031
Grünbaum, F. Alberto
7
1996
Matrix differential equations and scalar polynomials satisfying higher order recursions. Zbl 1163.42009
Durán, Antonio J.; Grünbaum, F. Alberto
7
2009
On a family of 2-variable orthogonal Krawtchouk polynomials. Zbl 1220.33008
Grünbaum, F. Alberto; Rahman, Mizan
7
2010
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.
7
2013
Quantum Markov chains: recurrence, Schur functions and splitting rules. Zbl 1435.81106
Grünbaum, F. A.; Lardizabal, C. F.; Velázquez, L.
7
2020
Stochastic Darboux transformations for quasi-birth-and-death processes and urn models. Zbl 1479.60151
Grünbaum, F. Alberto; de la Iglesia, Manuel D.
7
2019
On the extension of uniformly continuous mappings. Zbl 0169.38801
Grünbaum, F.; Zarantonello, E. H.
6
1968
The square of a Gaussian process. Zbl 0244.60033
Grünbaum, F. Alberto
6
1972
A new kind of inequality for Bessel functions. Zbl 0304.33012
Grünbaum, F. Alberto
6
1973
Reflective prolate-spheroidal operators and the KP/KdV equations. Zbl 1462.35330
Casper, W. Riley; Grünbaum, F. Alberto; Yakimov, Milen; Zurrián, Ignacio
6
2019
A remark on Hilber’s matrix. Zbl 0484.15009
Gruenbaum, F. Alberto
5
1982
An urn model associated with Jacobi polynomials. Zbl 1188.60040
Grünbaum, F. Alberto
5
2010
Associated polynomials, spectral matrices and the bispectral problem. Zbl 0956.33007
Grünbaum, F. Alberto; Haine, Luc
5
1999
The prolate spheroidal phenomenon as a consequence of bispectrality. Zbl 1085.47056
Grünbaum, F. Alberto; Yakimov, Milen
5
2004
Diffuse tomography: The isotropic case. Zbl 0760.65109
Grünbaum, F. Alberto
5
1992
Time-and-band limiting for matrix orthogonal polynomials of Jacobi type. Zbl 1376.33010
Castro, M.; Grünbaum, F. A.
5
2017
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.
5
2007
Time and band limiting for matrix valued functions, an example. Zbl 1318.33018
Grünbaum, F. Alberto; Pacharoni, Inés; Zurrián, Ignacio Nahuel
5
2015
A further look at time-and-band limiting for matrix orthogonal polynomials. Zbl 1411.33008
Castro, M.; Grünbaum, F. A.; Pacharoni, I.; Zurrián, I.
5
2018
Bispectrality and time-band limiting: matrix-valued polynomials. Zbl 07236276
Grünbaum, F. Alberto; Pacharoni, Inés; Zurrián, Ignacio
5
2020
The Fourier transform and the discrete Fourier transform. Zbl 0674.65114
Auslander, Louis; Grünbaum, F. Alberto
4
1989
Block tridiagonal matrices and a beefed-up version of the Ehrenfest urn model. Zbl 1178.33008
Grünbaum, F. Alberto
4
2009
The Heisenberg inequality for the discrete Fourier transform. Zbl 1053.42009
Grünbaum, F. Alberto
4
2003
Linear operator pencils on Lie algebras and Laurent biorthogonal polynomials. Zbl 1071.33013
Grünbaum, F. A.; Vinet, Luc; Zhedanov, Alexei
4
2004
A property of Legendre polynomials. Zbl 0202.34301
Grünbaum, F. A.
4
1970
Birth and death processes and quantum spin chains. Zbl 1285.82028
Grünbaum, F. Alberto; Vinet, Luc; Zhedanov, Alexei
4
2013
The Rahman polynomials are bispectral. Zbl 1193.33027
Grünbaum, F. Alberto
3
2007
Discrete models of the harmonic oscillator and a discrete analogue of Gauss’ hypergeometric equation. Zbl 1003.33003
Grünbaum, F. Alberto
3
2001
A nonlinear inverse problem inspired by three-dimensional diffuse tomography. Zbl 1003.65146
Grünbaum, F. Alberto
3
2001
Explicit inversion formulas for a model in diffuse tomography. Zbl 1016.92021
Grünbaum, F. Alberto; Matusevich, Laura Felicia
3
2002
On the existence of a ”wave operator” for the Boltzmann equation. Zbl 0254.45018
Grünbaum, F. Alberto
3
1972
P. A. M. Dirac meets M. G. Krein: matrix orthogonal polynomials and Dirac’s equation. Zbl 1094.33011
Durán, Antonio J.; Grünbaum, F. Alberto
3
2006
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
3
1992
An urn model for the Jacobi-Piñeiro polynomials. Zbl 1517.60084
Grünbaum, F. Alberto; de la Iglesia, Manuel D.
3
2022
Quantum walks: Schur functions meet symmetry protected topological phases. Zbl 07463704
Cedzich, C.; Geib, T.; Grünbaum, F. A.; Velázquez, L.; Werner, A. H.; Werner, R. F.
2
2022
Commuting integral and differential operators and the master symmetries of the Korteweg-de Vries equation. Zbl 07375642
Grünbaum, F. Alberto
1
2021
Quantum Markov chains: recurrence, Schur functions and splitting rules. Zbl 1435.81106
Grünbaum, F. A.; Lardizabal, C. F.; Velázquez, L.
7
2020
Bispectrality and time-band limiting: matrix-valued polynomials. Zbl 07236276
Grünbaum, F. Alberto; Pacharoni, Inés; Zurrián, Ignacio
5
2020
Stochastic Darboux transformations for quasi-birth-and-death processes and urn models. Zbl 1479.60151
Grünbaum, F. Alberto; de la Iglesia, Manuel D.
7
2019
Reflective prolate-spheroidal operators and the KP/KdV equations. Zbl 1462.35330
Casper, W. Riley; Grünbaum, F. Alberto; Yakimov, Milen; Zurrián, Ignacio
6
2019
Algebraic Heun operator and band-time limiting. Zbl 1405.33025
Grünbaum, F. Alberto; Vinet, Luc; Zhedanov, Alexei
34
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.
25
2018
A generalization of Schur functions: applications to Nevanlinna functions, orthogonal polynomials, random walks and unitary and open quantum walks. Zbl 1464.47011
Grünbaum, F. A.; Velázquez, L.
9
2018
Stochastic LU factorizations, Darboux transformations and urn models. Zbl 1402.60090
Grünbaum, F. Alberto; de la Iglesia, Manuel D.
8
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.
5
2018
Some limit laws for quantum walks with applications to a version of the Parrondo paradox. Zbl 1398.81061
Machida, Takuya; Grünbaum, F. Alberto
3
2018
Tridiagonalization and the Heun equation. Zbl 1364.34126
Grünbaum, F. Alberto; Vinet, Luc; Zhedanov, Alexei
25
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.
9
2017
Time-and-band limiting for matrix orthogonal polynomials of Jacobi type. Zbl 1376.33010
Castro, M.; Grünbaum, F. A.
5
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.
23
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.
8
2016
Maximal Parrondo’s paradox for classical and quantum Markov chains. Zbl 1333.60158
Grünbaum, F. Alberto; Pejic, Michael
2
2016
The Darboux process and time-and-band limiting for matrix orthogonal polynomials. Zbl 1326.33013
Castro, M.; Grünbaum, F. A.
8
2015
Time and band limiting for matrix valued functions, an example. Zbl 1318.33018
Grünbaum, F. Alberto; Pacharoni, Inés; Zurrián, Ignacio Nahuel
5
2015
Quantum recurrence of a subspace and operator-valued Schur functions. Zbl 1296.37014
Bourgain, J.; Grünbaum, F. A.; Velázquez, L.; Wilkening, J.
26
2014
Some noncommutative matrix algebras arising in the bispectral problem. Zbl 1353.34104
Grünbaum, F. Alberto
3
2014
Recurrence for discrete time unitary evolutions. Zbl 1276.81087
Grünbaum, F. A.; Velázquez, L.; Werner, A. H.; Werner, R. F.
37
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.
7
2013
Birth and death processes and quantum spin chains. Zbl 1285.82028
Grünbaum, F. Alberto; Vinet, Luc; Zhedanov, Alexei
4
2013
The quantum walk of F. Riesz. Zbl 1316.81010
Grünbaum, F. Alberto; Velázquez, Luis
3
2013
On a seminal paper by Karlin and McGregor. Zbl 1383.60064
Castro, Mirta M.; Grünbaum, F. Alberto
3
2013
The CGMV method for quantum walks. Zbl 1252.82082
Cantero, M. J.; Grünbaum, F. A.; Moral, L.; Velázquez, L.
36
2012
One-dimensional quantum walks with one defect. Zbl 1251.81026
Cantero, M. J.; Grünbaum, F. A.; Moral, L.; Velázquez, L.
30
2012
Properties of matrix orthogonal polynomials via their Riemann-Hilbert characterization. Zbl 1242.42020
Grünbaum, F. Alberto; De La Iglesia, Manuel D.; Martínez-Finkelshtein, Andrei
15
2011
The Darboux process and a noncommutative bispectral problem: some explorations and challenges. Zbl 1263.34022
Grünbaum, F. Alberto
13
2011
A system of multivariable Krawtchouk polynomials and a probabilistic application. Zbl 1244.33003
Grünbaum, F. Alberto; Rahman, Mizan
11
2011
Matrix-valued Szegő polynomials and quantum random walks. Zbl 1186.81036
Cantero, M. J.; Moral, L.; Grünbaum, F. Alberto; Velázquez, L.
56
2010
On a family of 2-variable orthogonal Krawtchouk polynomials. Zbl 1220.33008
Grünbaum, F. Alberto; Rahman, Mizan
7
2010
An urn model associated with Jacobi polynomials. Zbl 1188.60040
Grünbaum, F. Alberto
5
2010
A spectral weight matrix for a discrete version of Walsh’s spider. Zbl 1202.33016
Grünbaum, F. Alberto
2
2010
The Karlin-McGregor formula for a variant of a discrete version of Walsh’s spider. Zbl 1187.37094
Grünbaum, F. Alberto
8
2009
Matrix differential equations and scalar polynomials satisfying higher order recursions. Zbl 1163.42009
Durán, Antonio J.; Grünbaum, F. Alberto
7
2009
Block tridiagonal matrices and a beefed-up version of the Ehrenfest urn model. Zbl 1178.33008
Grünbaum, F. Alberto
4
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.
17
2008
Random walks and orthogonal polynomials: some challenges. Zbl 1184.33004
Grünbaum, F. Alberto
16
2008
The noncommutative bispectral problem for operators of order one. Zbl 1157.39001
Castro, Mirta M.; Grünbaum, F. Alberto
3
2008
The algebra of differential operators associated to a weight matrix. Zbl 1120.33008
Grünbaum, F. Alberto; Tirao, Juan
27
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
12
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.
5
2007
The Rahman polynomials are bispectral. Zbl 1193.33027
Grünbaum, F. Alberto
3
2007
Occupation time for two dimensional Brownian motion in a wedge. Zbl 1129.60074
Grünbaum, F. Alberto; McGrouther, Caroline
2
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
18
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
3
2006
An identification problem for multiterminal networks: solving for the traffic matrix from input-output measurements. Zbl 1120.65005
Grünbaum, F. Alberto; Matusevich, Laura Felicia
1
2006
Structural formulas for orthogonal matrix polynomials satisfying second-order differential equations. I. Zbl 1097.42018
Durán, Antonio J.; Grünbaum, F. Alberto
31
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
22
2005
A survey on orthogonal matrix polynomials satisfying second order differential equations. Zbl 1060.42017
Durán, Antonio J.; Grünbaum, F. Alberto
22
2005
Orthogonal matrix polynomials, scalar-type Rodrigues formulas and Pearson equations. Zbl 1066.42018
Durán, Antonio J.; Grünbaum, F. Alberto
17
2005
Orthogonal matrix polynomials satisfying first order differential equations: a collection of instructive examples. Zbl 1100.42015
Castro, Mirta M.; Grünbaum, F. Alberto
17
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
13
2005
Orthogonal matrix polynomials satisfying second-order differential equations. Zbl 1073.33009
Durán, Antonio J.; Grünbaum, F. Alberto
48
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
9
2004
The prolate spheroidal phenomenon as a consequence of bispectrality. Zbl 1085.47056
Grünbaum, F. Alberto; Yakimov, Milen
5
2004
Linear operator pencils on Lie algebras and Laurent biorthogonal polynomials. Zbl 1071.33013
Grünbaum, F. A.; Vinet, Luc; Zhedanov, Alexei
4
2004
Diffuse tomography as a source of challenging nonlinear inverse problems for a general class of networks. Zbl 1062.92043
Grünbaum, F. Alberto
2
2004
A network tomography problem related to the hypercube. Zbl 1061.92041
Grünbaum, F. Alberto; Matusevich, Laura Felicia
1
2004
Matrix valued orthogonal polynomials of the Jacobi type. Zbl 1070.33011
Grünbaum, F. A.; Pacharoni, I.; Tirao, J.
38
2003
Matrix valued Jacobi polynomials. Zbl 1026.33008
Grünbaum, F. Alberto
34
2003
A noncommutative version of the bispectral problem. Zbl 1038.39012
Grünbaum, F. Alberto; Iliev, Plamen
8
2003
The Heisenberg inequality for the discrete Fourier transform. Zbl 1053.42009
Grünbaum, F. Alberto
4
2003
Matrix valued spherical functions associated to the complex projective plane. Zbl 0996.43013
Grünbaum, F. A.; Pacharoni, I.; Tirao, J.
52
2002
Discrete bispectral Darboux transformations from Jacobi operators. Zbl 1051.39020
Grünbaum, F. Alberto; Yakimov, Milen
38
2002
Heat kernel expansions on the integers. Zbl 0996.35077
Grünbaum, F. Alberto; Iliev, Plamen
12
2002
Matrix valued spherical functions associated to the three dimensional hyperbolic space. Zbl 1048.22005
Grünbaum, F. A.; Pacharoni, I.; Tirao, J.
9
2002
Explicit inversion formulas for a model in diffuse tomography. Zbl 1016.92021
Grünbaum, F. Alberto; Matusevich, Laura Felicia
3
2002
The bispectral problem: An overview. Zbl 0999.47018
Grünbaum, F. Alberto
24
2001
A matrix-valued solution to Bochner’s problem. Zbl 0990.22012
Grünbaum, F. A.; Pacharoni, I.; Tirao, J.
19
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
9
2001
Electrostatic interpretation for the zeros of certain polynomials and the Darboux process. Zbl 0989.42006
Grünbaum, F. Alberto
9
2001
Discrete models of the harmonic oscillator and a discrete analogue of Gauss’ hypergeometric equation. Zbl 1003.33003
Grünbaum, F. Alberto
3
2001
A nonlinear inverse problem inspired by three-dimensional diffuse tomography. Zbl 1003.65146
Grünbaum, F. Alberto
3
2001
Some functions that generalize the Krall-Laguerre polynomials. Zbl 0926.33007
Grünbaum, F. Alberto; Haine, Luc; Horozov, Emil
53
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
7
1999
Associated polynomials, spectral matrices and the bispectral problem. Zbl 0956.33007
Grünbaum, F. Alberto; Haine, Luc
5
1999
The Wilson bispectral involution: Some elementary examples. Zbl 0924.34074
Grünbaum, F. Alberto; Haine, Luc
2
1999
Variations on a theme of Heine and Stieltjes: An electrostatic interpretation of the zeros of certain polynomials. Zbl 0934.33012
Grünbaum, F. Alberto
33
1998
Some bispectral musings. Zbl 0944.34062
Grünbaum, F. Alberto
12
1998
Bispectral Darboux transformations: an extension of the Krall polynomials. Zbl 1125.37321
Grünbaum, F. Alberto; Haine, Luc
52
1997
A theorem of Bochner, revisited. Zbl 0868.35116
Grünbaum, F. Alberto; Haine, Luc
15
1997
Some functions that generalize the Askey-Wilson polynomials. Zbl 0871.33009
Grünbaum, F. Alberto; Haine, Luc
11
1997
On the Krall-Hermite and the Krall-Bessel polynomials. Zbl 0910.33004
Grünbaum, F. Alberto; Haine, Luc; Horozov, Emil
8
1997
How many parameters can one solve for in diffuse tomography? Zbl 0880.60105
Grünbaum, F. A.; Patch, S. K.
1
1997
On a \(q\)-analogue of Gauss equation and some \(q\)-Riccati equations. Zbl 0870.39003
Grünbaum, F. Alberto; Haine, Luc
1
1997
Orthogonal polynomials satisfying differential equations: The role of the Darboux transformation. Zbl 0865.33008
Grünbaum, F. Alberto; Haine, Luc
47
1996
The \(q\)-version of a theorem of Bochner. Zbl 0865.33012
Grünbaum, F. Alberto; Haine, Luc
36
1996
Band-time-band limiting integral operators and commuting differential operators. Zbl 0878.47031
Grünbaum, F. Alberto
7
1996
The use of higher-order invariants in the determination of generalized Patterson cyclotomic sets. Zbl 1176.82034
Grünbaum, F. Alberto; Moore, Calvin C.
8
1995
Time-band limiting and the bispectral problem. Zbl 0802.34086
Grünbaum, F. Alberto
16
1994
The use of Graßmann identities for inversion of a general model in diffuse tomography. Zbl 0795.92015
Grünbaum, F. Alberto; Patch, S. K.
1
1993
Diffuse tomography: The isotropic case. Zbl 0760.65109
Grünbaum, F. Alberto
5
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
3
1992
Diffuse tomography: Computational aspects of the isotropic case. Zbl 0760.65110
Grünbaum, F. Alberto; Zubelli, Jorge P.
3
1992
Some new explorations into the mystery of time and band limiting. Zbl 0778.05084
Grünbaum, F. Alberto
3
1992
...and 40 more Documents
all top 5

Cited by 835 Authors

61 Grünbaum, Francisco Alberto
38 Durán, Antonio José
38 Vinet, Luc
23 Domínguez de la Iglesia, Manuel
22 Iliev, Plamen
22 Zhedanov, Alexei S.
21 Marcellán Español, Francisco
17 Crampé, Nicolas
17 Velázquez, Luis
14 Fillman, Jake
14 Konno, Norio
14 Segawa, Etsuo
12 Mañas, Manuel
12 Román, Pablo Manuel
12 Suzuki, Akito
12 Terwilliger, Paul M.
11 Khorozov, Emil Ivanov
11 van Diejen, Jan Felipe
10 Koelink, Erik
10 Zubelli, Jorge P.
9 Bernard, Pierre-Antoine
9 Cedzich, Christopher
9 Damanik, David
9 Garza, Luis E.
9 Ismail, Mourad El-Houssieny
9 Lardizabal, Carlos F.
9 Milson, Robert
9 Pacharoni, Inés
9 Werner, Albert H.
8 Branquinho, Amílcar José Pinto Lopes
8 Cantero, María José
8 Ishkin, Khabir Kabirovich
8 Moral, Leandro
8 Tirao, Juan
8 Tsujimoto, Satoshi
7 Choque Rivero, Abdon Eddy
7 Emsiz, Erdal
7 Foulquié Moreno, Ana Pilar
7 Gómez-Ullate, David
7 Joye, Alain
7 Kasman, Alex
7 Kuijlaars, Arno B. J.
7 Ong, Darren C.
7 Werner, Reinhard F.
7 Zurrián, Ignacio Nahuel
6 Álvarez-Nodarse, Renato
6 Baseilhac, Pascal
6 Dette, Holger
6 Dueñas, Herbert
6 Fuentes, Edinson
6 Geib, T.
6 Georgieva, Irina
6 Haine, Luc
6 Mischler, Stéphane
6 Veselov, Alexander Petrovich
5 Atakishiev, Natig M.
5 Castro, Mirta M.
5 Chalykh, Oleg A.
5 Ciaurri, Óscar
5 Fehér, László Gy.
5 Gaboriaud, Julien
5 Maeda, Masaya
5 Poulain D’Andecy, Loïc
5 Previato, Emma
5 Roncal, Luz
5 Sakhnovich, Alexander L.
5 Yakimov, Milen T.
4 Alfaro García, Manuel
4 Alzer, Horst
4 Ariznabarreta, Gerardo
4 Berest, Yuri Yu.
4 Bergeron, Geoffroy
4 Bourget, Alain
4 Carlen, Eric Anders
4 Casper, W. Riley
4 De Los Ríos, Ana M.
4 Derevyagin, Maxim S.
4 Eisler, Viktor
4 Fernández, Lidia
4 García-Ardila, Juan Carlos
4 Grandati, Yves
4 Hofreither, Clemens
4 Huertas Cejudo, Edmundo José
4 Ito, Tatsuro
4 Juarez, Claudia
4 Kiumi, Chusei
4 Kwon, Kil Hyun
4 Lakey, Joseph D.
4 Martínez-Finkelshtein, Andrei
4 Odake, Satoru
4 Rezola, María Luisa
4 Tanaka, Yohei
4 Varona Malumbres, Juan Luis
4 Wada, Kazuyuki
4 Yang, Di
3 Alhaidari, Abdulaziz D.
3 Anosova, Olga
3 Area, Iván
3 Asch, Joachim
3 Atakishiyeva, Mesuma K.
...and 735 more Authors
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Cited in 208 Serials

47 Journal of Approximation Theory
46 Journal of Mathematical Analysis and Applications
36 Journal of Mathematical Physics
36 Quantum Information Processing
33 Journal of Computational and Applied Mathematics
30 Communications in Mathematical Physics
26 Linear Algebra and its Applications
23 Proceedings of the American Mathematical Society
19 Journal of Physics A: Mathematical and Theoretical
15 Letters in Mathematical Physics
14 Integral Transforms and Special Functions
13 Journal of Statistical Physics
13 Advances in Mathematics
11 Physica D
11 Constructive Approximation
11 Applied and Computational Harmonic Analysis
11 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications
10 Reviews in Mathematical Physics
10 The Journal of Fourier Analysis and Applications
9 Journal of Functional Analysis
9 Transactions of the American Mathematical Society
9 Advances in Applied Mathematics
9 Annales Henri Poincaré
8 Inverse Problems
8 Journal of High Energy Physics
7 Numerical Functional Analysis and Optimization
7 The Ramanujan Journal
6 Bulletin des Sciences Mathématiques
5 Nuclear Physics. B
5 Physics Letters. A
5 Annales de l’Institut Fourier
5 Studies in Applied Mathematics
5 Mathematical Physics, Analysis and Geometry
4 Communications on Pure and Applied Mathematics
4 Linear and Multilinear Algebra
4 Integral Equations and Operator Theory
4 Inventiones Mathematicae
4 Journal of Differential Equations
4 Results in Mathematics
4 SIAM Journal on Algebraic and Discrete Methods
4 Probability Theory and Related Fields
4 Applied Mathematics Letters
4 Journal of Mathematical Sciences (New York)
4 Interdisciplinary Information Sciences (IIS)
4 Inverse Problems and Imaging
4 Analysis and Mathematical Physics
3 Archive for Rational Mechanics and Analysis
3 Journal d’Analyse Mathématique
3 Mathematical Notes
3 Theoretical and Mathematical Physics
3 Annali di Matematica Pura ed Applicata. Serie Quarta
3 Applied Mathematics and Computation
3 Journal of Applied Probability
3 Journal of Multivariate Analysis
3 Numerische Mathematik
3 Siberian Mathematical Journal
3 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
3 Acta Applicandae Mathematicae
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 Difference Equations and Applications
3 Discrete and Continuous Dynamical Systems
3 Doklady Mathematics
3 Lobachevskii Journal of Mathematics
3 Journal of Nonlinear Mathematical Physics
3 Mediterranean Journal of Mathematics
3 Journal of Statistical Mechanics: Theory and Experiment
3 Complex Analysis and Operator Theory
3 Kinetic and Related Models
3 Quantum Studies: Mathematics and Foundations
2 Applicable Analysis
2 Journal of Computational Physics
2 Journal of Fluid Mechanics
2 Physica A
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 Number Theory
2 Publications of the Research Institute for Mathematical Sciences, Kyoto University
2 SIAM Journal on Numerical Analysis
2 Acta Mathematicae Applicatae Sinica. English Series
2 Journal of Scientific Computing
2 Signal Processing
2 SIAM Journal on Mathematical Analysis
2 SIAM Journal on Scientific Computing
2 The Journal of Analysis
2 St. Petersburg Mathematical Journal
2 Mathematical Problems in Engineering
2 Transformation Groups
2 Differential Equations
2 Bulletin of the Malaysian Mathematical Sciences Society. Second Series
2 Bulletin of the Brazilian Mathematical Society. New Series
2 Journal of Algebra and its Applications
...and 108 more Serials
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Cited in 55 Fields

296 Special functions (33-XX)
200 Harmonic analysis on Euclidean spaces (42-XX)
181 Quantum theory (81-XX)
133 Operator theory (47-XX)
119 Probability theory and stochastic processes (60-XX)
109 Statistical mechanics, structure of matter (82-XX)
103 Partial differential equations (35-XX)
101 Ordinary differential equations (34-XX)
79 Linear and multilinear algebra; matrix theory (15-XX)
76 Numerical analysis (65-XX)
75 Dynamical systems and ergodic theory (37-XX)
57 Difference and functional equations (39-XX)
38 Combinatorics (05-XX)
35 Nonassociative rings and algebras (17-XX)
29 Functions of a complex variable (30-XX)
28 Information and communication theory, circuits (94-XX)
26 Integral transforms, operational calculus (44-XX)
23 Topological groups, Lie groups (22-XX)
21 Functional analysis (46-XX)
19 Algebraic geometry (14-XX)
19 Approximations and expansions (41-XX)
19 Integral equations (45-XX)
19 Optics, electromagnetic theory (78-XX)
16 Real functions (26-XX)
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13 Biology and other natural sciences (92-XX)
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11 Global analysis, analysis on manifolds (58-XX)
11 Statistics (62-XX)
11 Fluid mechanics (76-XX)
9 Commutative algebra (13-XX)
7 Mechanics of particles and systems (70-XX)
6 Number theory (11-XX)
6 Group theory and generalizations (20-XX)
6 Potential theory (31-XX)
5 Measure and integration (28-XX)
5 General topology (54-XX)
4 Several complex variables and analytic spaces (32-XX)
4 Relativity and gravitational theory (83-XX)
3 History and biography (01-XX)
3 Convex and discrete geometry (52-XX)
3 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
3 Systems theory; control (93-XX)
2 Geometry (51-XX)
2 Geophysics (86-XX)
2 Operations research, mathematical programming (90-XX)
1 General and overarching topics; collections (00-XX)
1 Mathematical logic and foundations (03-XX)
1 General algebraic systems (08-XX)
1 Calculus of variations and optimal control; optimization (49-XX)
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1 Mechanics of deformable solids (74-XX)
1 Astronomy and astrophysics (85-XX)

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