Algebraic Heun operator and band-time limiting. (English) Zbl 1405.33025
The authors introduce the algebraic Heun operator which can be obtained from any pair of bispectral operators and apply it to construct commute differential operators in the theory of time and band limiting. The algebraic Heun operator generalizes the ordinary one. The Heun operators are introduced through a simple bilinear Ansatz in terms of tridiagonal operators related to the Askey scheme and then the authors consider differential operators instead of tridiagonal matrices and study the commuting properties of these operators with projectors onto an interval. They apply their approach to the case of classical polynomials and extend it to Bannai-Ito polynomials and anti-Krawtchouk polynomials.
Reviewer: Chrysoula G. Kokologiannaki (Patras)
MSC:
| 33D45 | Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) |
| 33D99 | Basic hypergeometric functions |
| 39B42 | Matrix and operator functional equations |
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