On Approximate Solution of Certain Equations

In this paper, we consider problems of discrete approximation of special integral operators with the Calderon–Zygmund kernel. We introduce discrete spaces and bounded discrete operators acting in these spaces; then we use these operators for the search for approximate solutions of the corresponding...

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Bibliographic Details
Published inJournal of mathematical sciences (New York, N.Y.) Vol. 257; no. 1; pp. 8 - 16
Main Author Vasilyev, A. V.
Format Journal Article
LanguageEnglish
Published New York Springer US 04.08.2021
Springer
Springer Nature B.V
Subjects
Algebra
Integrals
Mathematical analysis
Mathematics
Mathematics and Statistics
Operators (mathematics)
symbol
approximate solution
65R20
Calderon–Zygmund kernel
42B10
approximation measure
discrete operator
45G05
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Summary:In this paper, we consider problems of discrete approximation of special integral operators with the Calderon–Zygmund kernel. We introduce discrete spaces and bounded discrete operators acting in these spaces; then we use these operators for the search for approximate solutions of the corresponding equations. We state theorems on the solvability of equations with discrete operators, compare integral operators with their discrete analogs, and obtain estimates of errors of approximate solutions.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-021-05464-6