Time and band limiting for exceptional polynomials

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 wit...

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Bibliographic Details
Published in:Applied and computational harmonic analysis 2024-01, Vol.68, p.101600, Article 101600
Main Authors: Castro, M.M., Grünbaum, F.A., Zurrián, I.
Format: Article
Language:English
Subjects:
Exceptional polynomials
Time-band limiting
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Summary: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.
ISSN:1063-5203
1096-603X
DOI:10.1016/j.acha.2023.101600