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Time-and-band limiting for symmetric classical Dunkl orthogonal polynomials
Abstract
The problem of ''time and band limiting'' has been previously considered for expansions in orthonormal polynomials that are common eigenfunctions of some second order differential operator. In this paper we consider the situation of orthonormal polynomials that are eigenfunctions of some second order differential-difference operator as introduced by Ch. Dunkl. These polynomials appear already in the work of G. Szegő and at the same time play a role in supersymmetric quantum mechanics.
Related
- Ratio and limiting zero distribution asymptotics for symmetric multiple orthogonal polynomials
- The manufacture of examples: the (−1)-classical orthogonal polynomials
- The manufacture of examples II: the "para-classical" orthogonal polynomials
- Matrix orthogonal polynomials related to diffference operators for L-orthogonal polynomials
- Identities and congruences involving orthogonal polynomials and Apéry-like numbers
BibTeX
@misc{castro2026timeandband,
title = {{Time-and-band limiting for symmetric classical Dunkl orthogonal polynomials}},
author = {M. M. Castro and F. A. Grünbaum},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.24100},
eprint = {2610.24100},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.24100},
}
RIS
TY - UNPB
TI - Time-and-band limiting for symmetric classical Dunkl orthogonal polynomials
AU - M. M. Castro
AU - F. A. Grünbaum
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2610.24100
UR - https://arxiv.org/abs/2610.24100
AB - The problem of ''time and band limiting'' has been previously considered for expansions in orthonormal polynomials that are common eigenfunctions of some second order differential operator. In this paper we consider the situation of orthonormal polynomials that are eigenfunctions of some second order differential-difference operator as introduced by Ch. Dunkl. These polynomials appear already in the work of G. Szegő and at the same time play a role in supersymmetric quantum mechanics.
ER -