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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
Received: 01.09.1998

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}


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