V. V. Volchkov, Vit. V. Volchkov, “Approximation of functions on rays in <nobr>$\Bbb{R}^n$</nobr> by solutions to convolution equations”, Sibirsk. Mat. Zh., 2023, Volume 64, Number 1,Pages <nobr>56

This article is cited in 3 papers

Approximation of functions on rays in $\Bbb{R}^n$ by solutions to convolution equations

V. V. Volchkov, Vit. V. Volchkov

Donetsk National University

Abstract: This is a first study of approximation of continuous functions on rays in $\Bbb{R}^n$ by smooth solutions to a multidimensional convolution equation with a radial convolutor. We obtain an analog of the well-known Carleman's Theorem on tangent approximation by entire functions. As consequences, we give some new results of interest for the theory of convolution equations. These results concern the density in $\Bbb{C}$ of the range of some solutions to the convolution equation as well as the possible growth of solutions on rays in $\Bbb{R}^n$.

Keywords: convolution equation, mean periodicity, Carleman's theorem.

UDC: 517.551

Received: 06.02.2022
Revised: 07.06.2022
Accepted: 15.08.2022

DOI: 10.33048/smzh.2023.64.105