Open AccessGeneralized localization for spherical partial sums of multiple Fourier series
Author(s) -
Ravshan Ashurov
Publication year - 2019
Publication title -
doklady akademii nauk. rossijskaâ akademiâ nauk
Language(s) - English
Resource type - Journals
ISSN - 0869-5652
DOI - 10.31857/s0869-565248917-10
Subject(s) - mathematics , fourier series , series (stratigraphy) , mathematical analysis , class (philosophy) , fourier transform , function (biology) , zero (linguistics) , open set , pure mathematics , combinatorics , computer science , biology , paleontology , linguistics , philosophy , artificial intelligence , evolutionary biology
In this paper the generalized localization principle for the spherical partial sums of the multiple Fourier series in the L2-class is proved, that is, if f L2 (ТN) and f = 0 on an open set ТN then it is shown that the spherical partial sums of this function converge to zero almost - everywhere on . It has been previously known that the generalized localization is not valid in Lp (TN) when 1 p 2. Thus the problem of generalized localization for the spherical partial sums is completely solved in Lp (TN), p 1: if p 2 then we have the generalized localization and if p 2, then the generalized localization fails.