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Title: The convergence of double Fourier-Haar series over homothetic copies of sets

Abstract

The paper is concerned with the convergence of double Fourier- Haar series with partial sums taken over homothetic copies of a given bounded set W⊂R{sub +}{sup 2} containing the intersection of some neighbourhood of the origin with R{sub +}{sup 2}. It is proved that for a set W from a fairly broad class (in particular, for convex W) there are two alternatives: either the Fourier-Haar series of an arbitrary function f∈L([0,1]{sup 2}) converges almost everywhere or Lln{sup +} L([0,1]{sup 2}) is the best integral class in which the double Fourier-Haar series converges almost everywhere. Furthermore, a characteristic property is obtained, which distinguishes which of the two alternatives is realized for a given W. Bibliography: 12 titles. (paper)

Authors:
 [1]
  1. Tseriteli State University, Kutaisi, Georgia (United States)
Publication Date:
OSTI Identifier:
22364932
Resource Type:
Journal Article
Resource Relation:
Journal Name: Sbornik. Mathematics; Journal Volume: 205; Journal Issue: 7; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; CALCULATION METHODS; CONVERGENCE; FUNCTIONS; INTEGRALS; MATHEMATICAL SOLUTIONS

Citation Formats

Oniani, G. G., E-mail: oniani@atsu.edu.ge. The convergence of double Fourier-Haar series over homothetic copies of sets. United States: N. p., 2014. Web. doi:10.1070/SM2014V205N07ABEH004406.
Oniani, G. G., E-mail: oniani@atsu.edu.ge. The convergence of double Fourier-Haar series over homothetic copies of sets. United States. doi:10.1070/SM2014V205N07ABEH004406.
Oniani, G. G., E-mail: oniani@atsu.edu.ge. Thu . "The convergence of double Fourier-Haar series over homothetic copies of sets". United States. doi:10.1070/SM2014V205N07ABEH004406.
@article{osti_22364932,
title = {The convergence of double Fourier-Haar series over homothetic copies of sets},
author = {Oniani, G. G., E-mail: oniani@atsu.edu.ge},
abstractNote = {The paper is concerned with the convergence of double Fourier- Haar series with partial sums taken over homothetic copies of a given bounded set W⊂R{sub +}{sup 2} containing the intersection of some neighbourhood of the origin with R{sub +}{sup 2}. It is proved that for a set W from a fairly broad class (in particular, for convex W) there are two alternatives: either the Fourier-Haar series of an arbitrary function f∈L([0,1]{sup 2}) converges almost everywhere or Lln{sup +} L([0,1]{sup 2}) is the best integral class in which the double Fourier-Haar series converges almost everywhere. Furthermore, a characteristic property is obtained, which distinguishes which of the two alternatives is realized for a given W. Bibliography: 12 titles. (paper)},
doi = {10.1070/SM2014V205N07ABEH004406},
journal = {Sbornik. Mathematics},
number = 7,
volume = 205,
place = {United States},
year = {Thu Jul 31 00:00:00 EDT 2014},
month = {Thu Jul 31 00:00:00 EDT 2014}
}