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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]:
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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2013, Issue 1(30), Pages 70–81 (Mi vsgtu1139)  

This article is cited in 4 scientific papers (total in 4 papers)

Procedings of the 3nd International Conference "Mathematical Physics and its Applications"
Equations of Mathematical Physics

The Dunkl convolution operators and multipoint de la Vallée–Poussin problem

K. R. Zabirovaa, V. V. Napalkovb

a Ufa State Aviation Technical University, Ufa, 450000, Russia
b Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences, Ufa, 450077, Russia

Abstract: The Dunkl operator as an object of mathematical physics is considered, we study the kernel and the surjectivity of Dunkl convolution operators in the space of entire functions and the space of entire functions of exponential type. The main result is the solution of the multipoint de la Vallée–Poussin problem for Dunkl convolution operators in the space of entire functions.

Keywords: Dunkl operators, Dunkl convolution, de la Vallée–Poussin (Cauchy) problem, sufficient sets, space of entire functions

DOI: https://doi.org/10.14498/vsgtu1139

Full text: PDF file (205 kB) (published under the terms of the Creative Commons Attribution 4.0 International License)
References: PDF file   HTML file

Bibliographic databases:

UDC: 517.53+517.98
MSC: Primary 47B38; Secondary 46A20, 46E10, 43A22, 30H05
Original article submitted 17/X/2012
revision submitted – 19/I/2013

Citation: K. R. Zabirova, V. V. Napalkov, “The Dunkl convolution operators and multipoint de la Vallée–Poussin problem”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 1(30) (2013), 70–81

Citation in format AMSBIB
\Bibitem{ZabNap13}
\by K.~R.~Zabirova, V.~V.~Napalkov
\paper The Dunkl convolution operators and multipoint de la Vall\'ee--Poussin problem
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2013
\vol 1(30)
\pages 70--81
\mathnet{http://mi.mathnet.ru/vsgtu1139}
\crossref{https://doi.org/10.14498/vsgtu1139}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. K. R. Zimens, V. V. Napalkov, “the Multiple de La Vallee-Poussin Problem on Convex Domains in the Kernel of the Convolution Operator”, Dokl. Math., 90:2 (2014), 581–583  crossref  crossref  mathscinet  zmath  isi  elib  elib  scopus
    2. V. V. Napalkov, A. U. Mullabaeva, “Kratnaya interpolyatsionnaya zadacha Valle Pussena”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 19:1 (2015), 63–77  mathnet  crossref  zmath  elib
    3. V. V. Napalkov, K. R. Zimens, “Zadacha Valle Pussena v yadre operatora svertki na poluploskosti”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 19:2 (2015), 283–292  mathnet  crossref  zmath  elib
    4. K. R. Zabirova, V. V. Napalkov, “Composition Operators of Convolution and Multiplication by a Function”, Math. Notes, 99:3 (2016), 368–377  mathnet  crossref  crossref  mathscinet  isi  elib
  • Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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