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Ufa Mathematical Journal, 2014, Volume 6, Issue 1, Pages 56–65
DOI: https://doi.org/10.13108/2014-6-1-56 (Mi ufa232) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Generalized Dunkl operator

I. I. Karamova, V. V. Napalkovb

a Ufa State Aviation Technical University, Ufa, Russia
b Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences, Ufa, Russia
English version PDF (335 kB) Citations (3) Russian version article
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DOI: https://doi.org/10.13108/2014-6-1-56
Abstract: In the paper we introduce a generalized Dunkl operator acting in the space of entire functions on C. We study problems of harmonic analysis related with this operator and show its connection with the Gelfond–Leont'ev operator of generalized differentiation.
Keywords: Dunkl operator, eigenfunction, Dunkl convolution operator, Dunkl transform, characteristic function, hypercyclic operator.
Received: 26.12.2013
Bibliographic databases:
Document Type: Article
UDC: 917.53+917.98
MSC: 47B38
Language: English
Original paper language: Russian
Citation: I. I. Karamov, V. V. Napalkov, “Generalized Dunkl operator”, Ufa Math. J., 6:1 (2014), 56–65
Citation in format AMSBIB
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\by I.~I.~Karamov, V.~V.~Napalkov
\paper Generalized Dunkl operator
\jour Ufa Math. J.
\yr 2014
\vol 6
\issue 1
\pages 56--65
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Linking options:
  • https://www.mathnet.ru/eng/ufa232
  • https://doi.org/10.13108/2014-6-1-56
  • https://www.mathnet.ru/eng/ufa/v6/i1/p59
    • This publication is cited in the following 3 articles:
    1. S. Hassanabadi, J. Kříž, B. C. Lütfüoğlu, W. S. Chung, P. Sedaghatnia, H. Hassanabadi, “Solutions of the Generalized Dunkl-Schrödinger Equation for Harmonic and Coulomb Potentials in two Dimensions”, Int J Theor Phys, 63:12 (2024)  crossref
    2. S Hassanabadi, J Kříž, B C Lütfüoğlu, H Hassanabadi, “Relativistic solutions of generalized-Dunkl harmonic and anharmonic oscillators”, Phys. Scr., 97:12 (2022), 125305  crossref
    3. A. V. Bratishchev, “On Gelfond–Leontiev Operators of Generalized Differentiation”, J. Math. Sci. (N. Y.), 252:3 (2021), 319–344  mathnet  crossref  mathscinet
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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    Statistics & downloads:
    Abstract page:487
    Russian version PDF:238
    English version PDF:49
    References:79
     
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