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Matematicheskie Zametki, 2011, Volume 89, Issue 3, Pages 323–330
DOI: https://doi.org/10.4213/mzm4992 (Mi mzm4992) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Generalization of the Multiplicative Fourier Transform and Its Properties

S. S. Volosivets

Saratov State University named after N. G. Chernyshevsky
Full-text PDF (428 kB) Citations (3)
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DOI: https://doi.org/10.4213/mzm4992
Abstract: We consider a new class of functions on the semiaxis for which the multiplicative Fourier transform can be defined. We prove equalities of Parseval type, an inversion formula and a condition for the validity of representation in the form of the multiplicative Fourier transform.
Keywords: multiplicative Fourier transform, Parseval equality, Dirichlet kernel, Fubini's theorem, Riesz–Torin theorem, dominated convergence.
Received: 12.05.2008
English version:
Mathematical Notes, 2011, Volume 89, Issue 3, Pages 311–318
DOI: https://doi.org/10.1134/S0001434611030011
Bibliographic databases:
Document Type: Article
UDC: 517.51
Language: Russian
Citation: S. S. Volosivets, “Generalization of the Multiplicative Fourier Transform and Its Properties”, Mat. Zametki, 89:3 (2011), 323–330; Math. Notes, 89:3 (2011), 311–318
Citation in format AMSBIB
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\by S.~S.~Volosivets
\paper Generalization of the Multiplicative Fourier Transform and Its Properties
\jour Mat. Zametki
\yr 2011
\vol 89
\issue 3
\pages 323--330
\mathnet{http://mi.mathnet.ru/mzm4992}
\crossref{https://doi.org/10.4213/mzm4992}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2856713}
\transl
\jour Math. Notes
\yr 2011
\vol 89
\issue 3
\pages 311--318
\crossref{https://doi.org/10.1134/S0001434611030011}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-79955622331}
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  • https://www.mathnet.ru/eng/mzm4992
  • https://doi.org/10.4213/mzm4992
  • https://www.mathnet.ru/eng/mzm/v89/i3/p323
    • This publication is cited in the following 3 articles:
    1. S. S. Volosivets, “Generalized Multiple Multiplicative Fourier Transform and Estimates of Integral Moduli of Continuity”, Math. Notes, 115:4 (2024), 528–537  mathnet  crossref  crossref  mathscinet
    2. Volosivets S.S. Kuznetsova M.A., “Generalized P-Adic Fourier Transform and Estimates of Integral Modulus of Continuity in Terms of This Transform”, P-Adic Numbers Ultrametric Anal. Appl., 10:4 (2018), 312–321  crossref  mathscinet  isi  scopus
    3. B. I. Golubov, S. S. Volosivets, Industrial and Applied Mathematics, Industrial Mathematics and Complex Systems, 2017, 129  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические заметки Mathematical Notes
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    Full-text PDF :208
    References:71
    First page:23
     
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