Generalized Dunkl operator

Authors

  • I.I. Karamov
    Ufa State Aviation Technical University, Ufa, Russia
  • V.V. Napalkov
    Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences, Ufa, Russia

DOI:

https://doi.org/10.13108/2014-6-1-56

Keywords:

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

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.

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Published

20.03.2014

Issue

Vol. 6 No. 1 (2014): Ufa Mathematical Journal 2014, volume 6 , issue 1

Section

Article