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Vestnik Yuzhno-Ural'skogo Gosudarstvennogo Universiteta. Seriya "Matematika. Mekhanika. Fizika", 2021, Volume 13, Issue 4, Pages 13–23
DOI: https://doi.org/10.14529/mmph210402
(Mi vyurm496)
 

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

Mathematics

Existence and uniqueness conditions for solutions of linear functional equations in the classes of Lebesgue functions antiderivatives on a simple smooth curve

V. L. Dilman, D. A. Komissarova

South Ural State University, Chelyabinsk, Russian Federation
Full-text PDF (642 kB) Citations (3)
References:
Abstract: The article describes linear functional equations on simple smooth curves with a shift function and fixed points only at the ends of the curve. The case when the shift function has a nonzero derivative satisfying the Hölder condition is considered. The objective of the article is to find the conditions of the existence and uniqueness of such equations solution in the classes of Lebesgue functions antiderivatives with a coefficient and the right-hand part belonging to the same classes. These conditions depend on the values of the equation coefficient at the ends of the curve. It is shown that if the coefficient and the right-hand side of a functional equation belong to the class of Lebesgue functions antiderivatives, then its solution also belongs to this class. The indicators of Hölder and of classes of Lebesgue functions antiderivatives are determined for the solutions. The research method is based on F. Riesz's criterion of a function's belonging to the class of antiderivatives of Lebesgue integrable functions. The possibilities of applying linear functional equations for studying and solving singular integral equations with logarithmic singularities are shown.
Keywords: singular integral equations with a shift, linear functional equations with a single variable, classes of Lebesgue functions antiderivatives.
Received: 22.10.2021
Document Type: Article
UDC: 517.965
Language: Russian
Citation: V. L. Dilman, D. A. Komissarova, “Existence and uniqueness conditions for solutions of linear functional equations in the classes of Lebesgue functions antiderivatives on a simple smooth curve”, Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz., 13:4 (2021), 13–23
Citation in format AMSBIB
\Bibitem{DilKom21}
\by V.~L.~Dilman, D.~A.~Komissarova
\paper Existence and uniqueness conditions for solutions of linear functional equations in the classes of Lebesgue functions antiderivatives on a simple smooth curve
\jour Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz.
\yr 2021
\vol 13
\issue 4
\pages 13--23
\mathnet{http://mi.mathnet.ru/vyurm496}
\crossref{https://doi.org/10.14529/mmph210402}
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  • https://www.mathnet.ru/eng/vyurm496
  • https://www.mathnet.ru/eng/vyurm/v13/i4/p13
  • This publication is cited in the following 3 articles:
    1. V. L. Dilman, T. V. Karpeta, “Nepreryvnye resheniya lineinykh funktsionalnykh uravnenii na kusochno-gladkikh krivykh v matematicheskikh modelyakh kraevykh zadach so sdvigom”, J. Comp. Eng. Math., 11:2 (2024), 11–21  mathnet  crossref
    2. V. L. Dilman, D. A. Komissarova, “Lineinye funktsionalnye uravneniya v klassakh pervoobraznykh ot lebegovskikh funktsii na otrezkakh krivykh”, Chelyab. fiz.-matem. zhurn., 8:1 (2023), 5–17  mathnet  crossref  mathscinet
    3. V. L. Dilman, “Svoistva i opisanie mnozhestv reshenii lineinykh funktsionalnykh uravnenii na prostoi gladkoi krivoi”, Vestn. Yuzhno-Ur. un-ta. Ser. Matem. Mekh. Fiz., 15:4 (2023), 5–13  mathnet  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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    Abstract page:142
    Full-text PDF :39
    References:34
     
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