Geodesic
On the degree of convergence of Borel and Euler means for double Fourier series of functions of bounded variation in Hardy sense
Mathematica Bohemica, Tome 120 (1995) no. 1, pp. 1-12

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

MR Zbl
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.
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.
DOI : 10.21136/MB.1995.125893
Classification : 42A20, 42B05, 42B08
Keywords: rate of convergence; bounded variation; rectangular partial sums; double Fourier series; double trigonometric series; Borel means; Euler means 
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, Tome 120 (1995) no. 1, pp. 1-12. doi: 10.21136/MB.1995.125893
@article{10_21136_MB_1995_125893,
     author = {Topolewska, Maria},
     title = {On the degree of convergence of {Borel} and {Euler} means for double {Fourier} series of functions of bounded variation in {Hardy} sense},
     journal = {Mathematica Bohemica},
     pages = {1--12},
     year = {1995},
     volume = {120},
     number = {1},
     doi = {10.21136/MB.1995.125893},
     mrnumber = {1336942},
     zbl = {0849.42009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.1995.125893/}
}
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
SP  - 1
EP  - 12
VL  - 120
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.1995.125893/
DO  - 10.21136/MB.1995.125893
LA  - en
ID  - 10_21136_MB_1995_125893
ER  - 
%0 Journal Article
%A Topolewska, Maria
%T On the degree of convergence of Borel and Euler means for double Fourier series of functions of bounded variation in Hardy sense
%J Mathematica Bohemica
%D 1995
%P 1-12
%V 120
%N 1
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.1995.125893/
%R 10.21136/MB.1995.125893
%G en
%F 10_21136_MB_1995_125893

[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. | MR

[2] C. K. Chui A. S. B. Holland: On the order of approximation by Euler and Taylor means. Journal of Approximation Theory 39 (1983), 24-38. | DOI | MR

[3] G. H. Hardy: Divergent series. Oxford, 1949. | MR | Zbl

[4] J. Marcinkiewicz: On a class of functions and their Fourier series. Collected papers. PWN, Warszawa, 1964, pp. 36-41.

[5] R. Taberski: On double integrals and Fourier series. Annales Polon. Math. 15 (1964), 97-115. | DOI | MR | Zbl

[6] L. Tonelli: Série Trigonometrische. Bologna, 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. | MR | Zbl

Cité par Sources :