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Some problems in the theory of multiple trigonometric series. (English. Russian original) Zbl 0784.42009
Russ. Math. Surv. 47, No. 5, 103-171 (1992); translation from Usp. Mat. Nauk 47, No. 5, 97-162 (1992).
This is a survey paper on the results of the field indicated in the title, which were published during the last decade. The table of contents: Introduction, Ch. I. Convergence of rectangular partial sums, Ch. II. New results on rectangular means of multiple Fourier series, Ch. III. Dirichlet kernels, Ch. IV. Uniqueness problems for multiple trigonometric series (rectangular partial sums), Ch. V. Problems of localization for rectangular partial sums, Ch. VI. Special classes of multiple trigonometric series, Ch. VII. A definition of convergence of multiple series, Ch. VIII. Conjugate series and conjugate functions of several variables, Ch. IX. Representation of functions by trigonometric series and “correction” of functions, Ch. X. Fourier coefficients, References contain 333 items.
The paper is warmly recommended to everyone who makes research in or wants to keep pace with the latest developments of this field.
Reviewer: F.Móricz (Szeged)

42B05 Fourier series and coefficients in several variables
42-02 Research exposition (monographs, survey articles) pertaining to harmonic analysis on Euclidean spaces
42B08 Summability in several variables
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