Edit Profile Grünbaum, Francisco Alberto Compute Distance To: Compute 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 all top 5 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 all top 5 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 all top 5 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) Publications by Year all cited Publications top 5 cited Publications 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 0625.34007Duistermaat, J. J.; Grünbaum, F. A. 137 1986 Bispectral Darboux transformations: an extension of the Krall polynomials. Zbl 1125.37321Grünbaum, F. Alberto; Haine, Luc 46 1997 Some functions that generalize the Krall-Laguerre polynomials. Zbl 0926.33007Grünbaum, F. Alberto; Haine, Luc; Horozov, Emil 41 1999 Matrix-valued Szegő polynomials and quantum random walks. Zbl 1186.81036Cantero, M. J.; Moral, L.; Grünbaum, F. Alberto; Velázquez, L. 40 2010 Orthogonal polynomials satisfying differential equations: The role of the Darboux transformation. Zbl 0865.33008Grünbaum, F. Alberto; Haine, Luc 40 1996 Matrix valued spherical functions associated to the complex projective plane. Zbl 0996.43013Grünbaum, F. A.; Pacharoni, I.; Tirao, J. 39 2002 Orthogonal matrix polynomials satisfying second-order differential equations. Zbl 1073.33009Durán, Antonio J.; Grünbaum, F. Alberto 38 2004 The \(q\)-version of a theorem of Bochner. Zbl 0865.33012Grünbaum, F. Alberto; Haine, Luc 34 1996 Matrix valued orthogonal polynomials of the Jacobi type. Zbl 1070.33011Grünbaum, F. A.; Pacharoni, I.; Tirao, J. 33 2003 Matrix valued Jacobi polynomials. Zbl 1026.33008Grünbaum, F. Alberto 33 2003 Variations on a theme of Heine and Stieltjes: An electrostatic interpretation of the zeros of certain polynomials. Zbl 0934.33012Grünbaum, F. Alberto 30 1998 Discrete bispectral Darboux transformations from Jacobi operators. Zbl 1051.39020Grünbaum, F. Alberto; Yakimov, Milen 28 2002 Propagation of chaos for the Boltzmann equation. Zbl 0236.45011Grünbaum, F. Alberto 26 1971 Recurrence for discrete time unitary evolutions. Zbl 1276.81087Grünbaum, F. A.; Velázquez, L.; Werner, A. H.; Werner, R. F. 24 2013 The algebra of differential operators associated to a weight matrix. Zbl 1120.33008Grünbaum, F. Alberto; Tirao, Juan 24 2007 Differential operators commuting with finite convolution integral operators: Some non-Abelian examples. Zbl 0497.22012Gruenbaum, F. A.; Longhi, L.; Perlstadt, M. 24 1982 The CGMV method for quantum walks. Zbl 1252.82082Cantero, M. J.; Grünbaum, F. A.; Moral, L.; Velázquez, L. 23 2012 One-dimensional quantum walks with one defect. Zbl 1251.81026Cantero, M. J.; Grünbaum, F. A.; Moral, L.; Velázquez, L. 23 2012 Structural formulas for orthogonal matrix polynomials satisfying second-order differential equations. I. Zbl 1097.42018Durán, Antonio J.; Grünbaum, F. Alberto 23 2005 Matrix valued orthogonal polynomials of Jacobi type: the role of group representation theory. Zbl 1082.33006Grünbaum, F. Alberto; Pacharoni, Inés; Tirao, Juan Alfredo 20 2005 Eigenvectors of a Toeplitz matrix: Discrete version of the prolate spheroidal wave functions. Zbl 0519.47019Gruenbaum, F. Alberto 19 1981 Tomographic reconstruction with arbitrary directions. Zbl 0441.93031Davison, M. E.; Grünbaum, F. Alberto 18 1981 The algebra of differential operators associated to a family of matrix-valued orthogonal polynomials: five instructive examples. Zbl 1130.33004Castro, Mirta M.; Grünbaum, F. Alberto 16 2006 A survey on orthogonal matrix polynomials satisfying second order differential equations. Zbl 1060.42017Durán, Antonio J.; Grünbaum, F. Alberto 16 2005 A matrix-valued solution to Bochner’s problem. Zbl 0990.22012Grünbaum, F. A.; Pacharoni, I.; Tirao, J. 16 2001 The eigenvectors of the discrete Fourier transform: A version of the Hermite functions. Zbl 0516.65099Gruenbaum, F. Alberto 16 1982 Quantum recurrence of a subspace and operator-valued Schur functions. Zbl 1296.37014Bourgain, J.; Grünbaum, F. A.; Velázquez, L.; Wilkening, J. 15 2014 Toeplitz matrices commuting with tridiagonal matrices. Zbl 0477.15005Gruenbaum, F. Alberto 15 1981 Tridiagonalization and the Heun equation. Zbl 1364.34126Grünbaum, F. Alberto; Vinet, Luc; Zhedanov, Alexei 14 2017 The bispectral problem: An overview. Zbl 0999.47018Grünbaum, F. Alberto 14 2001 A theorem of Bochner, revisited. Zbl 0868.35116Grünbaum, F. Alberto; Haine, Luc 14 1997 Orthogonal matrix polynomials, scalar-type Rodrigues formulas and Pearson equations. Zbl 1066.42018Durán, Antonio J.; Grünbaum, F. Alberto 13 2005 Commuting pairs of linear ordinary differential operators of orders four and six. Zbl 0654.47027Grünbaum, F. Alberto 13 1988 A new property of reproducing kernels for classical orthogonal polynomials. Zbl 0562.33008Grünbaum, F. Alberto 13 1983 Matrix valued orthogonal polynomials arising from group representation theory and a family of quasi-birth-and-death processes. Zbl 1163.60033Grünbaum, F. Alberto; de la Iglesia, Manuel D. 12 2008 Orthogonal matrix polynomials satisfying first order differential equations: a collection of instructive examples. Zbl 1100.42015Castro, Mirta M.; Grünbaum, F. Alberto 12 2005 Some bispectral musings. Zbl 0944.34062Grünbaum, F. Alberto 12 1998 Time-band limiting and the bispectral problem. Zbl 0802.34086Grünbaum, F. Alberto 12 1994 A study of Fourier space methods for ”limited angle” image reconstruction. Zbl 0458.65105Grünbaum, F. Alberto 11 1980 Algebraic Heun operator and band-time limiting. Zbl 1405.33025Grünbaum, F. Alberto; Vinet, Luc; Zhedanov, Alexei 10 2018 The Darboux process and a noncommutative bispectral problem: some explorations and challenges. Zbl 1263.34022Grünbaum, F. Alberto 10 2011 Matrix orthogonal polynomials satisfying second-order differential equations: coping without help from group representation theory. Zbl 1221.42046Durán, Antonio J.; Grünbaum, F. Alberto 10 2007 A characterization for a class of weight matrices with orthogonal matrix polynomials satisfying second-order differential equations. Zbl 1102.42013Durán, Antonio J.; Grünbaum, F. Alberto 10 2005 Some functions that generalize the Askey-Wilson polynomials. Zbl 0871.33009Grünbaum, F. Alberto; Haine, Luc 10 1997 Bulk-edge correspondence of one-dimensional quantum walks. Zbl 1342.82064Cedzich, C.; Grünbaum, F. A.; Stahl, C.; Velázquez, L.; Werner, A. H.; Werner, R. F. 9 2016 An invitation to matrix-valued spherical functions: Linearization of products in the case of complex projective space \(P_2(\mathbb C)\). Zbl 1075.33004Grünbaum, F. Alberto; Pacharoni, Inés; Tirao, Juan 9 2004 Heat kernel expansions on the integers. Zbl 0996.35077Grünbaum, F. Alberto; Iliev, Plamen 9 2002 A system of multivariable Krawtchouk polynomials and a probabilistic application. Zbl 1244.33003Grünbaum, F. Alberto; Rahman, Mizan 8 2011 Random walks and orthogonal polynomials: some challenges. Zbl 1184.33004Grünbaum, F. Alberto 8 2008 Matrix valued spherical functions associated to the three dimensional hyperbolic space. Zbl 1048.22005Grünbaum, F. A.; Pacharoni, I.; Tirao, J. 8 2002 On a \(q\)-analogue of the string equation and a generalization of the classical orthogonal polynomials. Zbl 0938.33010Grünbaum, F. Alberto; Haine, Luc 8 1999 Commuting differential operators for the finite Laplace transform. Zbl 0603.44002Bertero, M.; Grünbaum, F. A. 8 1985 Properties of matrix orthogonal polynomials via their Riemann-Hilbert characterization. Zbl 1242.42020Grünbaum, F. Alberto; De La Iglesia, Manuel D.; Martínez-Finkelshtein, Andrei 7 2011 Electrostatic interpretation for the zeros of certain polynomials and the Darboux process. Zbl 0989.42006Grünbaum, F. Alberto 7 2001 On a family of 2-variable orthogonal Krawtchouk polynomials. Zbl 1220.33008Grünbaum, F. Alberto; Rahman, Mizan 6 2010 Matrix-valued orthogonal polynomials related to \(\mathrm{SU}(N+1)\), their algebras of differential operators, and the corresponding curves. Zbl 1149.33002Grünbaum, F. Alberto; de la Iglesia, Manuel D. 6 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 0988.00112Bertero, Mario (ed.); Caputo, Jean Guy (ed.); Grünbaum, F. Alberto (ed.); Natterer, Frank (ed.) 6 2001 On the Krall-Hermite and the Krall-Bessel polynomials. Zbl 0910.33004Grünbaum, F. Alberto; Haine, Luc; Horozov, Emil 6 1997 A new kind of inequality for Bessel functions. Zbl 0304.33012Grünbaum, F. Alberto 6 1973 The square of a Gaussian process. Zbl 0244.60033Grünbaum, F. Alberto 6 1972 Linearization for the Boltzmann equation. Zbl 0236.45012Grünbaum, F. Alberto 6 1972 The topological classification of one-dimensional symmetric quantum walks. Zbl 1391.82027Cedzich, C.; Geib, T.; Grünbaum, F. A.; Stahl, C.; Velázquez, L.; Werner, A. H.; Werner, R. F. 5 2018 A quantum dynamical approach to matrix Khrushchev’s formulas. Zbl 1371.30004Cedzich, C.; Grünbaum, F. A.; Velázquez, L.; Werner, A. H.; Werner, R. F. 5 2016 The Darboux process and time-and-band limiting for matrix orthogonal polynomials. Zbl 1326.33013Castro, M.; Grünbaum, F. A. 5 2015 Two stochastic models of a random walk in the \(\mathrm U(n)\)-spherical duals of \(U(n+1)\). Zbl 1279.60010Grünbaum, F. A.; Pacharoni, I.; Tirao, J. 5 2013 The Karlin-McGregor formula for a variant of a discrete version of Walsh’s spider. Zbl 1187.37094Grünbaum, F. Alberto 5 2009 Matrix differential equations and scalar polynomials satisfying higher order recursions. Zbl 1163.42009Durán, Antonio J.; Grünbaum, F. Alberto 5 2009 The prolate spheroidal phenomenon as a consequence of bispectrality. Zbl 1085.47056Grünbaum, F. Alberto; Yakimov, Milen 5 2004 A noncommutative version of the bispectral problem. Zbl 1038.39012Grünbaum, F. Alberto; Iliev, Plamen 5 2003 The use of higher-order invariants in the determination of generalized Patterson cyclotomic sets. Zbl 1176.82034Grünbaum, F. Alberto; Moore, Calvin C. 5 1995 Differential operators commuting with convolution integral operators. Zbl 0506.45018Grünbaum, F. Alberto 5 1983 A remark on Hilber’s matrix. Zbl 0484.15009Gruenbaum, F. Alberto 5 1982 The Heisenberg inequality for the discrete Fourier transform. Zbl 1053.42009Grünbaum, F. Alberto 4 2003 Band-time-band limiting integral operators and commuting differential operators. Zbl 0878.47031Grünbaum, F. Alberto 4 1996 Diffuse tomography: The isotropic case. Zbl 0760.65109Grünbaum, F. Alberto 4 1992 The Fourier transform and the discrete Fourier transform. Zbl 0674.65114Auslander, Louis; Grünbaum, F. Alberto 4 1989 A property of Legendre polynomials. Zbl 0202.34301Grünbaum, F. A. 4 1970 On the extension of uniformly continuous mappings. Zbl 0169.38801Grünbaum, F.; Zarantonello, E. H. 4 1968 A further look at time-and-band limiting for matrix orthogonal polynomials. Zbl 1411.33008Castro, M.; Grünbaum, F. A.; Pacharoni, I.; Zurrián, I. 3 2018 Stochastic LU factorizations, Darboux transformations and urn models. Zbl 1402.60090Grünbaum, F. Alberto; de la Iglesia, Manuel D. 3 2018 Time and band limiting for matrix valued functions: an integral and a commuting differential operator. Zbl 1367.47078Grünbaum, F. A.; Pacharoni, I.; Zurrián, I. 3 2017 Time and band limiting for matrix valued functions, an example. Zbl 1318.33018Grünbaum, F. Alberto; Pacharoni, Inés; Zurrián, Ignacio Nahuel 3 2015 Birth and death processes and quantum spin chains. Zbl 1285.82028Grünbaum, F. Alberto; Vinet, Luc; Zhedanov, Alexei 3 2013 An urn model associated with Jacobi polynomials. Zbl 1188.60040Grünbaum, F. Alberto 3 2010 The noncommutative bispectral problem for operators of order one. Zbl 1157.39001Castro, Mirta M.; Grünbaum, F. Alberto 3 2008 P. A. M. Dirac meets M. G. Krein: matrix orthogonal polynomials and Dirac’s equation. Zbl 1094.33011Durán, Antonio J.; Grünbaum, F. Alberto 3 2006 The Wilson bispectral involution: Some elementary examples. Zbl 0924.34074Grünbaum, F. Alberto; Haine, Luc 3 1999 Some new explorations into the mystery of time and band limiting. Zbl 0778.05084Grünbaum, F. Alberto 3 1992 Diffuse tomography: Computational aspects of the isotropic case. Zbl 0760.65110Grünbaum, F. Alberto; Zubelli, Jorge P. 3 1992 On sets of differences. Zbl 0377.60025Grünbaum, F. Alberto 3 1977 On the existence of a ”wave operator” for the Boltzmann equation. Zbl 0254.45018Grünbaum, F. Alberto 3 1972 Stochastic Darboux transformations for quasi-birth-and-death processes and urn models. Zbl 07096794Grünbaum, F. Alberto; de la Iglesia, Manuel D. 2 2019 The quantum walk of F. Riesz. Zbl 1316.81010Grünbaum, F. Alberto; Velázquez, Luis 2 2013 On a seminal paper by Karlin and McGregor. Zbl 1383.60064Castro, Mirta M.; Grünbaum, F. Alberto 2 2013 Block tridiagonal matrices and a beefed-up version of the Ehrenfest urn model. Zbl 1178.33008Grünbaum, F. Alberto 2 2009 The Rahman polynomials are bispectral. Zbl 1193.33027Grünbaum, F. Alberto 2 2007 Diffuse tomography as a source of challenging nonlinear inverse problems for a general class of networks. Zbl 1062.92043Grünbaum, F. Alberto 2 2004 Linear operator pencils on Lie algebras and Laurent biorthogonal polynomials. Zbl 1071.33013Grünbaum, F. A.; Vinet, Luc; Zhedanov, Alexei 2 2004 Explicit inversion formulas for a model in diffuse tomography. Zbl 1016.92021Grünbaum, F. Alberto; Matusevich, Laura Felicia 2 2002 Discrete models of the harmonic oscillator and a discrete analogue of Gauss’ hypergeometric equation. Zbl 1003.33003Grünbaum, F. Alberto 2 2001 Bispectrality and time-band limiting: matrix-valued polynomials. Zbl 07236276Grünbaum, F. Alberto; Pacharoni, Inés; Zurrián, Ignacio 1 2020 Stochastic Darboux transformations for quasi-birth-and-death processes and urn models. Zbl 07096794Grünbaum, F. Alberto; de la Iglesia, Manuel D. 2 2019 Algebraic Heun operator and band-time limiting. Zbl 1405.33025Grünbaum, F. Alberto; Vinet, Luc; Zhedanov, Alexei 10 2018 The topological classification of one-dimensional symmetric quantum walks. Zbl 1391.82027Cedzich, C.; Geib, T.; Grünbaum, F. A.; Stahl, C.; Velázquez, L.; Werner, A. H.; Werner, R. F. 5 2018 A further look at time-and-band limiting for matrix orthogonal polynomials. Zbl 1411.33008Castro, M.; Grünbaum, F. A.; Pacharoni, I.; Zurrián, I. 3 2018 Stochastic LU factorizations, Darboux transformations and urn models. Zbl 1402.60090Grünbaum, F. Alberto; de la Iglesia, Manuel D. 3 2018 Some limit laws for quantum walks with applications to a version of the Parrondo paradox. Zbl 1398.81061Machida, Takuya; Grünbaum, F. Alberto 1 2018 A generalization of Schur functions: applications to Nevanlinna functions, orthogonal polynomials, random walks and unitary and open quantum walks. Zbl 06833446Grünbaum, F. A.; Velázquez, L. 1 2018 Tridiagonalization and the Heun equation. Zbl 1364.34126Grünbaum, F. Alberto; Vinet, Luc; Zhedanov, Alexei 14 2017 Time and band limiting for matrix valued functions: an integral and a commuting differential operator. Zbl 1367.47078Grünbaum, F. A.; Pacharoni, I.; Zurrián, I. 3 2017 Time-and-band limiting for matrix orthogonal polynomials of Jacobi type. Zbl 1376.33010Castro, M.; Grünbaum, F. A. 1 2017 Bulk-edge correspondence of one-dimensional quantum walks. Zbl 1342.82064Cedzich, C.; Grünbaum, F. A.; Stahl, C.; Velázquez, L.; Werner, A. H.; Werner, R. F. 9 2016 A quantum dynamical approach to matrix Khrushchev’s formulas. Zbl 1371.30004Cedzich, C.; Grünbaum, F. A.; Velázquez, L.; Werner, A. H.; Werner, R. F. 5 2016 Maximal Parrondo’s paradox for classical and quantum Markov chains. Zbl 1333.60158Grünbaum, F. Alberto; Pejic, Michael 1 2016 The Darboux process and time-and-band limiting for matrix orthogonal polynomials. Zbl 1326.33013Castro, M.; Grünbaum, F. A. 5 2015 Time and band limiting for matrix valued functions, an example. Zbl 1318.33018Grünbaum, F. Alberto; Pacharoni, Inés; Zurrián, Ignacio Nahuel 3 2015 Quantum recurrence of a subspace and operator-valued Schur functions. Zbl 1296.37014Bourgain, J.; Grünbaum, F. A.; Velázquez, L.; Wilkening, J. 15 2014 Some noncommutative matrix algebras arising in the bispectral problem. Zbl 1353.34104Grünbaum, F. Alberto 1 2014 Recurrence for discrete time unitary evolutions. Zbl 1276.81087Grünbaum, F. A.; Velázquez, L.; Werner, A. H.; Werner, R. F. 24 2013 Two stochastic models of a random walk in the \(\mathrm U(n)\)-spherical duals of \(U(n+1)\). Zbl 1279.60010Grünbaum, F. A.; Pacharoni, I.; Tirao, J. 5 2013 Birth and death processes and quantum spin chains. Zbl 1285.82028Grünbaum, F. Alberto; Vinet, Luc; Zhedanov, Alexei 3 2013 The quantum walk of F. Riesz. Zbl 1316.81010Grünbaum, F. Alberto; Velázquez, Luis 2 2013 On a seminal paper by Karlin and McGregor. Zbl 1383.60064Castro, Mirta M.; Grünbaum, F. Alberto 2 2013 The CGMV method for quantum walks. Zbl 1252.82082Cantero, M. J.; Grünbaum, F. A.; Moral, L.; Velázquez, L. 23 2012 One-dimensional quantum walks with one defect. Zbl 1251.81026Cantero, M. J.; Grünbaum, F. A.; Moral, L.; Velázquez, L. 23 2012 The Darboux process and a noncommutative bispectral problem: some explorations and challenges. Zbl 1263.34022Grünbaum, F. Alberto 10 2011 A system of multivariable Krawtchouk polynomials and a probabilistic application. Zbl 1244.33003Grünbaum, F. Alberto; Rahman, Mizan 8 2011 Properties of matrix orthogonal polynomials via their Riemann-Hilbert characterization. Zbl 1242.42020Grünbaum, F. Alberto; De La Iglesia, Manuel D.; Martínez-Finkelshtein, Andrei 7 2011 Matrix-valued Szegő polynomials and quantum random walks. Zbl 1186.81036Cantero, M. J.; Moral, L.; Grünbaum, F. Alberto; Velázquez, L. 40 2010 On a family of 2-variable orthogonal Krawtchouk polynomials. Zbl 1220.33008Grünbaum, F. Alberto; Rahman, Mizan 6 2010 An urn model associated with Jacobi polynomials. Zbl 1188.60040Grünbaum, F. Alberto 3 2010 The Karlin-McGregor formula for a variant of a discrete version of Walsh’s spider. Zbl 1187.37094Grünbaum, F. Alberto 5 2009 Matrix differential equations and scalar polynomials satisfying higher order recursions. Zbl 1163.42009Durán, Antonio J.; Grünbaum, F. Alberto 5 2009 Block tridiagonal matrices and a beefed-up version of the Ehrenfest urn model. Zbl 1178.33008Grünbaum, F. Alberto 2 2009 Matrix valued orthogonal polynomials arising from group representation theory and a family of quasi-birth-and-death processes. Zbl 1163.60033Grünbaum, F. Alberto; de la Iglesia, Manuel D. 12 2008 Random walks and orthogonal polynomials: some challenges. Zbl 1184.33004Grünbaum, F. Alberto 8 2008 The noncommutative bispectral problem for operators of order one. Zbl 1157.39001Castro, Mirta M.; Grünbaum, F. Alberto 3 2008 The algebra of differential operators associated to a weight matrix. Zbl 1120.33008Grünbaum, F. Alberto; Tirao, Juan 24 2007 Matrix orthogonal polynomials satisfying second-order differential equations: coping without help from group representation theory. Zbl 1221.42046Durán, Antonio J.; Grünbaum, F. Alberto 10 2007 Matrix-valued orthogonal polynomials related to \(\mathrm{SU}(N+1)\), their algebras of differential operators, and the corresponding curves. Zbl 1149.33002Grünbaum, F. Alberto; de la Iglesia, Manuel D. 6 2007 The Rahman polynomials are bispectral. Zbl 1193.33027Grünbaum, F. Alberto 2 2007 The algebra of differential operators associated to a family of matrix-valued orthogonal polynomials: five instructive examples. Zbl 1130.33004Castro, Mirta M.; Grünbaum, F. Alberto 16 2006 P. A. M. Dirac meets M. G. Krein: matrix orthogonal polynomials and Dirac’s equation. Zbl 1094.33011Durán, Antonio J.; Grünbaum, F. Alberto 3 2006 Structural formulas for orthogonal matrix polynomials satisfying second-order differential equations. I. Zbl 1097.42018Durán, Antonio J.; Grünbaum, F. Alberto 23 2005 Matrix valued orthogonal polynomials of Jacobi type: the role of group representation theory. Zbl 1082.33006Grünbaum, F. Alberto; Pacharoni, Inés; Tirao, Juan Alfredo 20 2005 A survey on orthogonal matrix polynomials satisfying second order differential equations. Zbl 1060.42017Durán, Antonio J.; Grünbaum, F. Alberto 16 2005 Orthogonal matrix polynomials, scalar-type Rodrigues formulas and Pearson equations. Zbl 1066.42018Durán, Antonio J.; Grünbaum, F. Alberto 13 2005 Orthogonal matrix polynomials satisfying first order differential equations: a collection of instructive examples. Zbl 1100.42015Castro, Mirta M.; Grünbaum, F. Alberto 12 2005 A characterization for a class of weight matrices with orthogonal matrix polynomials satisfying second-order differential equations. Zbl 1102.42013Durán, Antonio J.; Grünbaum, F. Alberto 10 2005 Orthogonal matrix polynomials satisfying second-order differential equations. Zbl 1073.33009Durán, Antonio J.; Grünbaum, F. Alberto 38 2004 An invitation to matrix-valued spherical functions: Linearization of products in the case of complex projective space \(P_2(\mathbb C)\). Zbl 1075.33004Grünbaum, F. Alberto; Pacharoni, Inés; Tirao, Juan 9 2004 The prolate spheroidal phenomenon as a consequence of bispectrality. Zbl 1085.47056Grünbaum, F. Alberto; Yakimov, Milen 5 2004 Diffuse tomography as a source of challenging nonlinear inverse problems for a general class of networks. Zbl 1062.92043Grünbaum, F. Alberto 2 2004 Linear operator pencils on Lie algebras and Laurent biorthogonal polynomials. Zbl 1071.33013Grünbaum, F. A.; Vinet, Luc; Zhedanov, Alexei 2 2004 Matrix valued orthogonal polynomials of the Jacobi type. Zbl 1070.33011Grünbaum, F. A.; Pacharoni, I.; Tirao, J. 33 2003 Matrix valued Jacobi polynomials. Zbl 1026.33008Grünbaum, F. Alberto 33 2003 A noncommutative version of the bispectral problem. Zbl 1038.39012Grünbaum, F. Alberto; Iliev, Plamen 5 2003 The Heisenberg inequality for the discrete Fourier transform. Zbl 1053.42009Grünbaum, F. Alberto 4 2003 Matrix valued spherical functions associated to the complex projective plane. Zbl 0996.43013Grünbaum, F. A.; Pacharoni, I.; Tirao, J. 39 2002 Discrete bispectral Darboux transformations from Jacobi operators. Zbl 1051.39020Grünbaum, F. Alberto; Yakimov, Milen 28 2002 Heat kernel expansions on the integers. Zbl 0996.35077Grünbaum, F. Alberto; Iliev, Plamen 9 2002 Matrix valued spherical functions associated to the three dimensional hyperbolic space. Zbl 1048.22005Grünbaum, F. A.; Pacharoni, I.; Tirao, J. 8 2002 Explicit inversion formulas for a model in diffuse tomography. Zbl 1016.92021Grünbaum, F. Alberto; Matusevich, Laura Felicia 2 2002 A matrix-valued solution to Bochner’s problem. Zbl 0990.22012Grünbaum, F. A.; Pacharoni, I.; Tirao, J. 16 2001 The bispectral problem: An overview. Zbl 0999.47018Grünbaum, F. Alberto 14 2001 Electrostatic interpretation for the zeros of certain polynomials and the Darboux process. Zbl 0989.42006Grünbaum, F. Alberto 7 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 0988.00112Bertero, Mario (ed.); Caputo, Jean Guy (ed.); Grünbaum, F. Alberto (ed.); Natterer, Frank (ed.) 6 2001 Discrete models of the harmonic oscillator and a discrete analogue of Gauss’ hypergeometric equation. Zbl 1003.33003Grünbaum, F. Alberto 2 2001 A nonlinear inverse problem inspired by three-dimensional diffuse tomography. Zbl 1003.65146Grünbaum, F. Alberto 2 2001 Some functions that generalize the Krall-Laguerre polynomials. Zbl 0926.33007Grünbaum, F. Alberto; Haine, Luc; Horozov, Emil 41 1999 On a \(q\)-analogue of the string equation and a generalization of the classical orthogonal polynomials. Zbl 0938.33010Grünbaum, F. Alberto; Haine, Luc 8 1999 The Wilson bispectral involution: Some elementary examples. Zbl 0924.34074Grünbaum, F. Alberto; Haine, Luc 3 1999 Associated polynomials, spectral matrices and the bispectral problem. Zbl 0956.33007Grünbaum, F. Alberto; Haine, Luc 2 1999 Variations on a theme of Heine and Stieltjes: An electrostatic interpretation of the zeros of certain polynomials. Zbl 0934.33012Grünbaum, F. Alberto 30 1998 Some bispectral musings. Zbl 0944.34062Grünbaum, F. Alberto 12 1998 Bispectral Darboux transformations: an extension of the Krall polynomials. Zbl 1125.37321Grünbaum, F. Alberto; Haine, Luc 46 1997 A theorem of Bochner, revisited. Zbl 0868.35116Grünbaum, F. Alberto; Haine, Luc 14 1997 Some functions that generalize the Askey-Wilson polynomials. Zbl 0871.33009Grünbaum, F. Alberto; Haine, Luc 10 1997 On the Krall-Hermite and the Krall-Bessel polynomials. Zbl 0910.33004Grünbaum, F. Alberto; Haine, Luc; Horozov, Emil 6 1997 On a \(q\)-analogue of Gauss equation and some \(q\)-Riccati equations. Zbl 0870.39003Grünbaum, F. Alberto; Haine, Luc 1 1997 How many parameters can one solve for in diffuse tomography? Zbl 0880.60105Grünbaum, F. A.; Patch, S. K. 1 1997 Orthogonal polynomials satisfying differential equations: The role of the Darboux transformation. Zbl 0865.33008Grünbaum, F. Alberto; Haine, Luc 40 1996 The \(q\)-version of a theorem of Bochner. Zbl 0865.33012Grünbaum, F. Alberto; Haine, Luc 34 1996 Band-time-band limiting integral operators and commuting differential operators. Zbl 0878.47031Grünbaum, F. Alberto 4 1996 The use of higher-order invariants in the determination of generalized Patterson cyclotomic sets. Zbl 1176.82034Grünbaum, F. Alberto; Moore, Calvin C. 5 1995 Time-band limiting and the bispectral problem. Zbl 0802.34086Grünbaum, F. Alberto 12 1994 The use of Graßmann identities for inversion of a general model in diffuse tomography. Zbl 0795.92015Grünbaum, F. Alberto; Patch, S. K. 1 1993 Diffuse tomography: The isotropic case. Zbl 0760.65109Grünbaum, F. Alberto 4 1992 Some new explorations into the mystery of time and band limiting. Zbl 0778.05084Grünbaum, F. Alberto 3 1992 Diffuse tomography: Computational aspects of the isotropic case. Zbl 0760.65110Grünbaum, F. Alberto; Zubelli, Jorge P. 3 1992 An inverse problem in transport theory: Diffuse tomography. Zbl 0789.60063Grünbaum, F. Alberto 1 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 0741.00059Grünbaum, F. Alberto (ed.); Bernfeld, Marvin (ed.); Blahut, Richard E. (ed.) 1 1992 Trying to beat Heisenberg. Zbl 0702.35199Grünbaum, F. Alberto 2 1990 Darboux’s method and some “rank two” explicit solutions of the KP equation. Zbl 0722.35080Grünbaum, F. A. 1 1990 Concentrating a potential and its scattering transform for a discrete version of the Schrödinger and Zakharov-Shabat operators. Zbl 0703.58053Grünbaum, F. Alberto 1 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 0691.00018Auslander, L. (ed.); Grünbaum, F. A. (ed.); Helton, J. W. (ed.); Kailath, T. (ed.); Khargoneka, P. (ed.); Mitter, S. (ed.) 1 1990 The Fourier transform and the discrete Fourier transform. Zbl 0674.65114Auslander, Louis; Grünbaum, F. Alberto 4 1989 The scattering problem for a phase-modulated hyperbolic secant pulse. Zbl 0698.35113Grünbaum, F. Alberto 1 1989 Commuting pairs of linear ordinary differential operators of orders four and six. Zbl 0654.47027Grünbaum, F. Alberto 13 1988 Differential equations in the spectral parameter. Zbl 0625.34007Duistermaat, J. J.; Grünbaum, F. A. 137 1986 ...and 33 more Documents all cited Publications top 5 cited Publications all top 5 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 all top 5 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. 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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. 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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 all top 5 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) Citations by Year