This article is cited in 3 papers

Dunkl–Darboux differential-difference operators

S. P. Khekalo

State Socio-Humanitarian University, Kolomna, Moscow region

Abstract: Using a natural generalization, we construct and study analogues of Dunkl differential-difference operators on the line. These analogues turn out to be closely connected with the so-called Burchnall–Chaundy–Adler–Moser polynomials and, therefore, with Darboux transforms. We find the eigenfunctions of these operators.

Keywords: differential-difference operators, rational Dunkl operators, Burchnall–Chaundy–Adler–Moser polynomials, eigenfunctions.

UDC: 517.929.2

MSC: 33C70, 33D50, 13N10, 37K10

Received: 21.04.2015
Revised: 18.03.2016

DOI: 10.4213/im8397

 English version: Izvestiya: Mathematics, 2017, 81:1, 156–178

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