On the degree of convergence of Borel and Euler means for double Fourier series of functions of bounded variation in Hardy sense

Maria Topolewska

Mathematica Bohemica (1995)

  • Volume: 120, Issue: 1, page 1-12
  • ISSN: 0862-7959

Abstract

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For real functions of bounded variation in the Hardy sense, 2 π -periodic in each variable, the rates of pointwise convergence of the Borel and Euler means of their Fourier series are estimated.

How to cite

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Topolewska, Maria. "On the degree of convergence of Borel and Euler means for double Fourier series of functions of bounded variation in Hardy sense." Mathematica Bohemica 120.1 (1995): 1-12. <http://eudml.org/doc/247809>.

@article{Topolewska1995,
abstract = {For real functions of bounded variation in the Hardy sense, $2\pi $-periodic in each variable, the rates of pointwise convergence of the Borel and Euler means of their Fourier series are estimated.},
author = {Topolewska, Maria},
journal = {Mathematica Bohemica},
keywords = {rate of convergence; bounded variation; rectangular partial sums; double Fourier series; double trigonometric series; Borel means; Euler means; rate of convergence; bounded variation; rectangular partial sums; double Fourier series},
language = {eng},
number = {1},
pages = {1-12},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the degree of convergence of Borel and Euler means for double Fourier series of functions of bounded variation in Hardy sense},
url = {http://eudml.org/doc/247809},
volume = {120},
year = {1995},
}

TY - JOUR
AU - Topolewska, Maria
TI - On the degree of convergence of Borel and Euler means for double Fourier series of functions of bounded variation in Hardy sense
JO - Mathematica Bohemica
PY - 1995
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 120
IS - 1
SP - 1
EP - 12
AB - For real functions of bounded variation in the Hardy sense, $2\pi $-periodic in each variable, the rates of pointwise convergence of the Borel and Euler means of their Fourier series are estimated.
LA - eng
KW - rate of convergence; bounded variation; rectangular partial sums; double Fourier series; double trigonometric series; Borel means; Euler means; rate of convergence; bounded variation; rectangular partial sums; double Fourier series
UR - http://eudml.org/doc/247809
ER -

References

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  1. R. Bojanić, An estimate of the rate of convergence for Fourier series of functions of bounded variation, Publications de L'Institut Mathématique, Nouvelle série 26(40) (1979), 57-60. (1979) MR0572330
  2. C. K. Chui A. S. B. Holland, 10.1016/0021-9045(83)90066-7, Journal of Approximation Theory 39 (1983), 24-38. (1983) MR0713359DOI10.1016/0021-9045(83)90066-7
  3. G. H. Hardy, Divergent series, Oxford, 1949. (1949) Zbl0032.05801MR0030620
  4. J. Marcinkiewicz, On a class of functions and their Fourier series, Collected papers. PWN, Warszawa, 1964, pp. 36-41. (1964) 
  5. R. Taberski, On double integrals and Fourier series, Annales Polon. Math. 15 (1964), 97-115. (1964) Zbl0171.30002MR0167787
  6. L. Tonelli, Série Trigonometrische, Bologna, 1928. (1928) 
  7. M. Topolewska, On the degree of convergence of Borel and Euler means of trigonometric series, Časopis pro pěstování matematiky 112(3) (1987), 225-232. (1987) Zbl0625.42004MR0905967

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