This article is cited in 3 papers

Generalized Dunkl operator

I. I. Karamov^a, V. V. Napalkov<sup>b

a</sup> Ufa State Aviation Technical University, Ufa, Russia
^b Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences, Ufa, Russia

Abstract: In the paper we introduce a generalized Dunkl operator acting in the space of entire functions on $\mathbb C$. We study problems of harmonic analysis related with this operator and show its connection with the Gelfond–Leont'ev operator of generalized differentiation.

Keywords: Dunkl operator, eigenfunction, Dunkl convolution operator, Dunkl transform, characteristic function, hypercyclic operator.

UDC: 917.53+917.98

MSC: 47B38

Received: 26.12.2013

 English version: Ufa Mathematical Journal, 2014, 6:1, 56–65

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