F. Alberto Grünbaum

Year appointed: 1974

Year retired: 2014

Selected Publications: 

1. F. A. Grünbaum, Time and band limiting: from the early days to the present, WSEAS Transactions on Systems, Vol 24, 2025. DOI 10.37394/23202.2025.24.30.
2. F. A. Grünbaum, A tribute to Henry P. McKean, jr. Notices AMS March 2025, vol 72 276--277.
3. W. R. Casper, F. A. Grünbaum, M. Yakimov and I. Zurrián, Matrix valued discrete-continous functions with the prolate spheroidal property and bispectrality, Comm. Math. Physics 405 (2024), no. 3.
4. M. Castro and F. A. Grünbaum, A new commutative property for exceptional orthogonal polynomials, Revista de la Academia de Ciencias, vol 118, article number 81, (2024).
5. W. R. Casper, F. A. Grünbaum, M. Yakimov and I. Zurrián, Reflective prolate-spheroidal operators and the adelic grassmanian, Comm. Pure and Applied Math, 76, 2023 pp 3679--3810.
6. W. R. Casper, F. A. Grünbaum, M. Yakimov and I. Zurrián, Algebras of commuting differential operators for kernels of Airy type, in memory of Harold Widom, Oper. Theory Adv. Applic. 289, Birhauser/Springer pp 229--256.
7. M. Castro, F. A. Grünbaum and I. Zurrián, Time and band limiting for exceptional polynomials, Applied and Computational Harmonic Analysis, Oct 2023.
8. F. A. Grünbaum, A Feyman-Kac approach to a paper of Chung and Feller on fluctuations in the coin tossing game, Proc. AMS 150, 2022, pp 4027--4036.
9. F. A. Grünbaum, Serendipity strikes again, PNAS 2022, vol 119, No. 26.
10. F. A. Grünbaum and M. de la Iglesia , An urn model for the Jacobi-Pigneiro polynomials, Proc AMS 150(2022) pp 3613-3625.
11. C. Cedzich, T. Gieb, F. A. Grünbaum, L. Velázquez, A. Werner, Quantumwalks: Schur functions meet symmetry protected topological phases, Comm. Math. Physics, 389, (2022) 1, 31--74.
12. F. A. Grünbaum, Commuting integral and differential operators and the master symmetries of the Korteweg-deVries equation, Inverse Problems 37 (2021), 8.
13. F. A. Grünbaum, Velázquez, L. and Wilkening J. Occupation time for classical and quantum walks, From operator theory to orthogonal polynomials, combinatorics and number theory-a volume in honor of Lance Littlejohn's 70th birthday, pp 197-212 Oper. Theory Adv. Appl. 285 Birkhauser/Springer, Cham 202 1.
14. F. A. Grünbaum, I. Pacharoni and I. Zurrián, Bispectrality and time-band limiting: matrix-valued polynomials, Int. Math. Res. Not. 2020, No. 13 (2020), 4016--4036.
15. Grünbaum, F. A.; Lardizabal, C. F.; Velázquez, L. Quantum Markov chains: recurrence, Schur functions and splitting rules. Ann. Henri Poincaré 21 (2020), no. 1, 189–239. 81P47 (81S22).
16. Casper, W. Riley; Grünbaum, F. Alberto; Yakimov, M.; Zurrián, I, Reflective prolate-spheroidal operators and the KP/KdV equations. PNAS September 10, 2019 116 (37) 18310-18315.
17. Grünbaum, F. Alberto; Vinet, Luc; Zhedanov, Alexei Algebraic Heun operator and band-time limiting. Comm. Math. Phys. 364 (2018), no. 3, 1041–1068.
18. Grünbaum, F. Alberto; de la Iglesia, Manuel D. Stochastic LU factorizations, Darboux transformations and urn models. J. Appl. Probab. 55 (2018), no. 3, 862–886. 60J10 (33C45 42C05).
19. Grünbaum, F. A.; Velázquez, L. A generalization of Schur functions: applications to Nevanlinna functions, orthogonal polynomials, random walks and unitary and open quantum walks. Adv. Math. 326 (2018), 352–464.
20. Cedzich,C.; Geib, T.; Grünbaum, F. A.; Stahl, C.; Velázquez, L.; Werner, A. H.;Werner, R. F. The topological classification of one-dimensional symmetric quantum walks. Ann. Henri Poincaré 19 (2018), no. 2, 325–383.     
21. Grünbaum, Francisco Alberto; Velázquez, Luis The CMV bispectral problem. Int. Math. Res. Not. IMRN 2017, no. 19, 5833–5860.  
22. Castro, M.; Grünbaum, F. A. Time-and-band limiting for matrix orthogonal polynomials of Jacobi type. Random Matrices Theory Appl. 6   (2017), no.4, 1740001, 12 pp.    
23. Grünbaum, F. A.; Pacharoni, I.; Zurrián, I. Time and band limiting for matrix valued functions: an integral and a commuting differential  operator. Inverse Problems 33 (2017), no. 2, 025005, 14 pp. 
24. Grünbaum, F. Alberto; Vinet, Luc; Zhedanov, Alexei Tridiagonalization and the Heun equation. J. Math. Phys. 58 (2017), no. 3, 031703,  12 pp. 
25. Cedzich, C.; Grünbaum, F. A.; Stahl, C.; Velázquez, L.; Werner, A. H.; Werner, R. F. Bulk-edge correspondence of one-dimensional quantum walks. J. Phys. A 49 (2016), no. 21, 21LT01, 12 pp. 81Q35.
26. Cedzich,C.; Grünbaum,  F. A.; Velázquez, L.; Werner, A. H.; Werner, R. F. A quantum dynamical approach to matrix Khrushchev's formulas. Comm. Pure Appl. Math. 69 (2016), no. 5, 909–957.
27. Grünbaum, F. Alberto; Pacharoni, Inés; Zurrián, Ignacio Nahuel Time and band limiting for matrix valued functions, an example. SIGMA Symmetry Integrability Geom. Methods Appl. 11 (2015), Paper 044, 14 pp. 42C10 .