Edit Profile (opens in new tab) Grünbaum, Francisco Alberto Co-Author Distance Author ID: grunbaum.francisco-alberto Published as: Grünbaum, F. Alberto; Grünbaum, F. A.; Gruenbaum, F. Alberto; Grünbaum, Francisco Alberto; Grünbaum, F.; Gruenbaum, F. A. more...less Homepage: https://math.berkeley.edu/people/faculty/f-alberto-gruenbaum External Links: MGP · GND Documents Indexed: 180 Publications since 1966, including 6 Additional arXiv Preprints 5 Contributions as Editor Co-Authors: 57 Co-Authors with 104 Joint Publications 1,394 Co-Co-Authors all top 5 Co-Authors 81 single-authored 15 Velázquez, Luis 11 Haine, Luc 11 Pacharoni, Inés 9 Castro, Mirta M. 9 Zurrián, Ignacio Nahuel 8 Durán, Antonio José 7 Tirao, Juan 7 Yakimov, Milen T. 6 Domínguez de la Iglesia, Manuel 5 Werner, Albert H. 5 Werner, Reinhard F. 4 Casper, W. Riley 4 Cedzich, Christopher 4 Vinet, Luc 4 Zhedanov, Alexei S. 4 Zubelli, Jorge P. 3 Cantero, María José 3 Matusevich, Laura Felicia 3 Moral, Leandro 2 Auslander, Louis 2 Bertero, Mario 2 Geib, T. 2 Hasenfeld, Andrew 2 Khorozov, Emil Ivanov 2 Iliev, Plamen 2 Machida, Takuya 2 Patch, Sarah K. 2 Rahman, Mizan 2 Wilkening, Jon A. 2 Zarantonello, Eduardo H. 1 Antoun, John T. 1 Bernfeld, Marvin 1 Blahut, Richard E. 1 Bourgain, Jean 1 Caputo, Jean-Guy 1 Davison, Mark E. 1 Duistermaat, Johannes Jisse 1 Feig, Ephraim 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 Martínez-Finkelshtein, Andrei 1 McGrouther, Caroline 1 McKean, Henry P. jun. 1 Mitter, Sanjoy K. 1 Moll, Victor Hugo 1 Moore, Calvin C. 1 Natterer, Frank 1 Pejic, Michael 1 Perlstadt, Marci A. 1 Singer, J. R. 1 Tirao, Juan Alfredo 1 van Moerbeke, Pierre 1 Vasquez, Brian D. 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 all cited Publications top 5 cited Publications 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 cited Publications top 5 cited Publications 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 all top 5 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. 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New Series 2 Journal of Algebra and its Applications ...and 108 more Serials all top 5 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) 15 Associative rings and algebras (16-XX) 14 Abstract harmonic analysis (43-XX) 13 Biology and other natural sciences (92-XX) 12 Differential geometry (53-XX) 12 Computer science (68-XX) 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) 1 Algebraic topology (55-XX) 1 Mechanics of deformable solids (74-XX) 1 Astronomy and astrophysics (85-XX) Citations by Year