Article
Time and band limiting for exceptional polynomials
Author/s | Castro Smirnova, Mirta María
![]() ![]() ![]() ![]() ![]() ![]() ![]() Grünbaum, Francisco Alberto Zurrián, Ignacio Nahuel |
Department | Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI) |
Publication Date | 2024-01 |
Deposit Date | 2024-07-04 |
Published in |
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Abstract | The "time-and-band limiting" commutative property was found and exploited by D. Slepian, H. Landau and H. Pollak at Bell Labs in the 1960's, and independently by M. Mehta and later by C. Tracy and H. Widom in Random matrix ... The "time-and-band limiting" commutative property was found and exploited by D. Slepian, H. Landau and H. Pollak at Bell Labs in the 1960's, and independently by M. Mehta and later by C. Tracy and H. Widom in Random matrix theory. The property in question is the existence of local operators with simple spectrum that commute with naturally appearing global ones. Here we give a general result that insures the existence of a commuting differential operator for a given family of exceptional orthogonal polynomials satisfying the "bispectral property". As a main tool we go beyond bispectrality and make use of the notion of Fourier Algebras associated to the given sequence of exceptional polynomials. We illustrate this result with two examples, of Hermite and Laguerre type, exhibiting also a nice Perline's form for the commuting differential operator. |
Funding agencies | European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER) Agencia Estatal de Investigación. España Junta de Andalucía Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET). Argentina Ministerio de Ciencia e Innovación Universidad de Sevilla |
Project ID. | PID2021-124332NB-C21
![]() FQM-262 ![]() 112-200801-01533 ![]() 30720150100255CB ![]() PID2021-124332NB-C21 ![]() USE-20357-W ![]() |
Citation | Castro Smirnova, M.M., Grünbaum, F.A. y Zurrián, I.N. (2024). Time and band limiting for exceptional polynomials. Applied and Computational Harmonic Analysis, 68 (101600). https://doi.org/10.1016/j.acha.2023.101600. |
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