Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2018, Volume 149, Pages 3–13 (Mi into312)  
This article is cited in 4 scientific papers (total in 4 papers)

Positivity Conditions for Operators with Difference Kernels in Reflexive Spaces

S. N. Askhabovab

a Chechen State Pedagogical Institute
b Chechen State University, Groznyi
Full-text PDF (222 kB) Citations (4)
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Abstract: Using methods of the theory of discrete and integral Fourier transforms, we obtain necessary and sufficient conditions of the positivity of linear discrete, integral, and integro-differential operators with difference kernels in the spaces ${\ell}_p$ and $L_p$ for $1<p <\infty$ and present examples illustrating the results obtained.
Keywords: positive operator, convolution operator, generalized operator of potential type, singular operator, integro-differential operator.
English version:
Journal of Mathematical Sciences (New York), 2020, Volume 250, Issue 5, Pages 717–727
DOI: https://doi.org/10.1007/s10958-020-05036-0
Bibliographic databases:
Document Type: Article
UDC: 517.983
MSC: 47G10, 47G20
Language: Russian
Citation: S. N. Askhabov, “Positivity Conditions for Operators with Difference Kernels in Reflexive Spaces”, Proceedings of the International Conference “Actual Problems of Applied Mathematics and Physics,” Kabardino-Balkaria, Nalchik, May 17–21, 2017, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 149, VINITI, Moscow, 2018, 3–13; J. Math. Sci. (N. Y.), 250:5 (2020), 717–727
Citation in format AMSBIB
\Bibitem{Ask18}
\by S.~N.~Askhabov
\paper Positivity Conditions for Operators with Difference Kernels in Reflexive Spaces
\inbook Proceedings of the International Conference ``Actual Problems of Applied Mathematics and Physics,'' Kabardino-Balkaria, Nalchik, May 17--21, 2017
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2018
\vol 149
\pages 3--13
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into312}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3847718}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2020
\vol 250
\issue 5
\pages 717--727
\crossref{https://doi.org/10.1007/s10958-020-05036-0}
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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