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Mathematics of the USSR-Izvestiya, 1969, Volume 3, Issue 3, Pages 633–642
DOI: https://doi.org/10.1070/IM1969v003n03ABEH000794
(Mi im2164)
 

This article is cited in 6 scientific papers (total in 6 papers)

Difference properties of functions of several variables

M. F. Timan
References:
Abstract: In this article, new identities are established for the so-called total, mixed, and partial differences of functions of several variables. As applications of these identities, expressions are given for mixed derivatives in terms of directional derivatives, as well as inequalities for total and mixed moduli of smoothness of continuous functions of $n$ variables. Moreover, it is shown that in the spaces $L_p$ $(1<p<\infty)$, the orders of decrease of the total modulus of smoothness and of the sum of the moduli of smoothness in the coordinate directions only are the same.
Received: 26.01.1968
Bibliographic databases:
UDC: 517.5
MSC: 35R10, 35B65, 39A05
Language: English
Original paper language: Russian
Citation: M. F. Timan, “Difference properties of functions of several variables”, Math. USSR-Izv., 3:3 (1969), 633–642
Citation in format AMSBIB
\Bibitem{Tim69}
\by M.~F.~Timan
\paper Difference properties of functions of several variables
\jour Math. USSR-Izv.
\yr 1969
\vol 3
\issue 3
\pages 633--642
\mathnet{http://mi.mathnet.ru//eng/im2164}
\crossref{https://doi.org/10.1070/IM1969v003n03ABEH000794}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=271282}
\zmath{https://zbmath.org/?q=an:0191.39002|0214.35203}
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  • https://doi.org/10.1070/IM1969v003n03ABEH000794
  • https://www.mathnet.ru/eng/im/v33/i3/p667
  • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
     
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