FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

1999, VOLUME 5, NUMBER 4, PAGES 1003-1013

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

M. I. Dyachenko

Abstract

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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 $C(Tm)$-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 $L(Tm)$-metric.

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Last modified: December 9, 1999