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 Fundam. Prikl. Mat.: Year: Volume: Issue: Page: Find

 Fundam. Prikl. Mat., 1999, Volume 5, Issue 4, Pages 1003–1013 (Mi fpm428)

The rate of Pringsheim convergence of multiple Fourier series of piecewise monotonic functions of many variables in the space $L$

M. I. Dyachenko

M. V. Lomonosov Moscow State University

Abstract: It has been earlier proved by the author that the Fourier series of piecewise monotonic functions of many variables converge in the sense of Pringsheim pointwise and in $C(T^m)$-metric faster than in the case of arbitrary continuous functions. The main result of the paper says that this is not valid for the Pringsheim convergence in $L(T^m)$-metric.

Full text: PDF file (319 kB)

Bibliographic databases:
UDC: 517.52

Citation: M. I. Dyachenko, “The rate of Pringsheim convergence of multiple Fourier series of piecewise monotonic functions of many variables in the space $L$”, Fundam. Prikl. Mat., 5:4 (1999), 1003–1013

Citation in format AMSBIB
\Bibitem{Dya99} \by M.~I.~Dyachenko \paper The~rate of Pringsheim convergence of multiple Fourier series of piecewise monotonic functions of many variables in the~space~$L$ \jour Fundam. Prikl. Mat. \yr 1999 \vol 5 \issue 4 \pages 1003--1013 \mathnet{http://mi.mathnet.ru/fpm428} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1782951} \zmath{https://zbmath.org/?q=an:0967.42005}