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Izv. RAN. Ser. Mat., 2017, Volume 81, Issue 1, Pages 161–182 (Mi izv8397)  

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.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-51-150005 НЦНИ_а
This paper was written with the financial support of RFBR (grant no. 16-51-150005 NCNI_a).


DOI: https://doi.org/10.4213/im8397

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

Bibliographic databases:

UDC: 517.929.2
MSC: 33C70, 33D50, 13N10, 37K10
Received: 21.04.2015
Revised: 18.03.2016

Citation: S. P. Khekalo, “Dunkl–Darboux differential-difference operators”, Izv. RAN. Ser. Mat., 81:1 (2017), 161–182; Izv. Math., 81:1 (2017), 156–178

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  • Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya Izvestiya: Mathematics
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