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Problemy Analiza — Issues of Analysis, 2021, Volume 10(28), Issue 3, Pages 129–140
DOI: https://doi.org/10.15393/j3.art.2021.10751
(Mi pa336)
 

This article is cited in 3 scientific papers (total in 3 papers)

Interpolation problems for functions with zero ball means

V. V. Volchkov, Vit. V. Volchkov

Donetsk National University, 24 Universitetskaya str., Donetsk 283001, Russia
Full-text PDF (575 kB) Citations (3)
References:
Abstract: Let $n\geq 2$, $V_r(\mathbb{R}^n)$ be the set of functions with zero integrals over all balls in $\mathbb{R}^n$ of radius $r$. Various interpolation problems for the class $V_r(\mathbb{R}^n)$ are studied. In the case when the set of interpolation nodes is finite, we solve the interpolation problem under general conditions. For the problems with infinite set of nodes, some sufficient conditions of solvability are founded.
Note that an essential condition is that the definition of the class $V_r(\mathbb{R}^n)$ involves integration over balls. For instance, it can be shown that the analogues of our results in which the class of functions is defined using zero integrals over all shifts of a fixed parallelepiped in $\mathbb{R}^n$ do not hold true.
Keywords: interpolation problems, spherical means, mean periodicity.
Received: 22.05.2021
Revised: 17.07.2021
Accepted: 03.08.2021
Bibliographic databases:
Document Type: Article
UDC: 517.444
MSC: 44A35, 45E10, 46F10
Language: English
Citation: V. V. Volchkov, Vit. V. Volchkov, “Interpolation problems for functions with zero ball means”, Probl. Anal. Issues Anal., 10(28):3 (2021), 129–140
Citation in format AMSBIB
\Bibitem{VolVol21}
\by V.~V.~Volchkov, Vit.~V.~Volchkov
\paper Interpolation problems for functions with zero ball means
\jour Probl. Anal. Issues Anal.
\yr 2021
\vol 10(28)
\issue 3
\pages 129--140
\mathnet{http://mi.mathnet.ru/pa336}
\crossref{https://doi.org/10.15393/j3.art.2021.10751}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000701564800001}
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  • https://www.mathnet.ru/eng/pa336
  • https://www.mathnet.ru/eng/pa/v28/i3/p129
  • This publication is cited in the following 3 articles:
    1. V. V. Volchkov, Vit. V. Volchkov, “Interpolation of Functions with Zero Spherical Averages Obeying Growth Constraints”, Sib Math J, 65:5 (2024), 1043  crossref
    2. V. V. Volchkov, Vit. V. Volchkov, “Interpolyatsiya funktsii s nulevymi sharovymi srednimi s ogranicheniem rosta”, Sib. matem. zhurn., 65:5 (2024), 841–851  mathnet  crossref
    3. V. V. Volchkov, Vit. V. Volchkov, “Interpolation Problem with Knots on a Line for Solutions of a Multidimensional Convolution Equation”, Lobachevskii J Math, 44:8 (2023), 3630  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Problemy Analiza — Issues of Analysis
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