This article is cited in 5 papers

Procedings of the 3nd International Conference "Mathematical Physics and its Applications"
Equations of Mathematical Physics

The Dunkl convolution operators and multipoint de la Vallée–Poussin problem

K. R. Zabirova^a, V. V. Napalkov<sup>b

a</sup> Ufa State Aviation Technical University, Ufa, 450000, Russia
^b Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences, Ufa, 450077, Russia

Abstract: The Dunkl operator as an object of mathematical physics is considered, we study the kernel and the surjectivity of Dunkl convolution operators in the space of entire functions and the space of entire functions of exponential type. The main result is the solution of the multipoint de la Vallée–Poussin problem for Dunkl convolution operators in the space of entire functions.

Keywords: Dunkl operators, Dunkl convolution, de la Vallée–Poussin (Cauchy) problem, sufficient sets, space of entire functions.

UDC: 517.53+517.98

MSC: Primary 47B38; Secondary 46A20, 46E10, 43A22, 30H05

Original article submitted 17/X/2012
revision submitted – 19/I/2013

DOI: 10.14498/vsgtu1139

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