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Matematicheskie Zametki, 2023, Volume 114, Issue 4, Pages 509–524
DOI: https://doi.org/10.4213/mzm14021 (Mi mzm14021) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Nondeformed Generalized Dunkl transform on the Line

V. I. Ivanovabc

a Lomonosov Moscow State University
b Moscow Center for Fundamental and Applied Mathematics
c Tula State University
Full-text PDF (626 kB) Citations (4)
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DOI: https://doi.org/10.4213/mzm14021
Abstract: A generalization of the Dunkl transform can be the $(k,a)$-generalized Fourier transform, but it deforms good classes of functions, for example, the Schwartz space. In this paper, we study the nondeformed generalized Dunkl transform on the line. Two generalized translation operators are defined. Integral representations are obtained for them and $L_p$-boundedness is proved. Two convolutions are defined for which the Young theorem is established. As an application, we study conditions for the $L_p$-convergence of generalized means.
Keywords: generalized Fourier transform, generalized Dunkl transform, generalized translation operator, convolutions and generalized means.
Funding agency Grant number
Russian Science Foundation 23-71-30001
This work was financially supported by the Russian Science Foundation, project 23-71-30001, https://rscf.ru/en/project/23-71-30001/.
Received: 01.05.2023
English version:
Mathematical Notes, 2023, Volume 114, Issue 4, Pages 443–456
DOI: https://doi.org/10.1134/S0001434623090171
Bibliographic databases:
Document Type: Article
UDC: 517.5
MSC: 42A38
Language: Russian
Citation: V. I. Ivanov, “Nondeformed Generalized Dunkl transform on the Line”, Mat. Zametki, 114:4 (2023), 509–524; Math. Notes, 114:4 (2023), 443–456
Citation in format AMSBIB
\Bibitem{Iva23}
\by V.~I.~Ivanov
\paper Nondeformed Generalized Dunkl transform on the Line
\jour Mat. Zametki
\yr 2023
\vol 114
\issue 4
\pages 509--524
\mathnet{http://mi.mathnet.ru/mzm14021}
\crossref{https://doi.org/10.4213/mzm14021}
\transl
\jour Math. Notes
\yr 2023
\vol 114
\issue 4
\pages 443--456
\crossref{https://doi.org/10.1134/S0001434623090171}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85174702215}
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  • https://doi.org/10.4213/mzm14021
  • https://www.mathnet.ru/eng/mzm/v114/i4/p509
    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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