V. V. Napalkov, A. U. Mullabaeva, “On one class of differential operators and their application”, Trudy Inst. Mat. i Mekh. UrO RAN, 2014, Volume 20, Number 1,Pages <nobr>201

This article is cited in 4 papers

On one class of differential operators and their application

V. V. Napalkov^a, A. U. Mullabaeva^b

^a Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences
^b Bashkir State University

Abstract: We use a generalized differentiation operator to construct a generalized shift operator, which makes it possible to define a generalized convolution operator in the space $H(\mathbb C)$. Next, we consider the characteristic function of this operator and introduce a generalized Laplace transform. We study the homogeneous equation of the generalized convolution operator, investigate its solvability, and consider the multi-point Vallée Poussin problem.

Keywords: generalized Bargmann–Fock space, generalized differentiation operator, eigenfunction, generalized Laplace transform, characteristic function, generalized shift operator, generalized convolution operator, sequentially sufficient set, uniqueness set, Vallée Poussin problem.

UDC: 517.977

Received: 18.04.2013