Back to Search Start Over

Some problems in the theory of multiple trigonometric series

Authors :
M I D'yachenko
Source :
Russian Mathematical Surveys. 47:103-171
Publication Year :
1992
Publisher :
IOP Publishing, 1992.

Abstract

CONTENTSIntroductionChapter I. Convergence of rectangular partial sums ?1. Results on the almost everywhere convergence of Fourier series of integrable functions ?2. The almost everywhere convergence of Fourier series of functions from ?3. A brief survey of new results on the convergence of rectangular partial sums in various metricsChapter II. New results on rectangular means of multiple Fourier seriesChapter III. Dirichlet kernels ?1. Lebesgue constants and norms of some trigonometric polynomials ?2. Asymptotic behaviour of Dirichlet kernelsChapter IV. Uniqueness problems for multiple trigonometric series (rectangular partial sums)Chapter V. Problems of localization for rectangular partial sumsChapter VI. Special classes of multiple trigonometric series ?1. Series with monotone coefficients ?2. Multiple lacunary series ?3. Fourier series of piecewise monotone functions of several variablesChapter VII. A definition of convergence of multiple seriesChapter VIII. Conjugate series and conjugate functions of several variables ?1. Conjugate series and conjugate functions in , ?2. The conjugation operator in the space ?3. Multidimensional analogues of Plessner's theoremChapter IX. Representation of functions by trigonometric series and correction of functionsChapter X. Fourier coefficients ?1. Cantor-Lebesgue and Denjoy-Luzin theorems ?2. New results on the absolute convergence of Fourier series ?3. Transformations of Fourier coefficients and other resultsReferences

Details

ISSN :
14684829 and 00360279
Volume :
47
Database :
OpenAIRE
Journal :
Russian Mathematical Surveys
Accession number :
edsair.doi...........1e218a285438bea184d9509ea87886f4
Full Text :
https://doi.org/10.1070/rm1992v047n05abeh000944