| Title:
|
On the degree of convergence of Borel and Euler means for double Fourier series of functions of bounded variation in Hardy sense (English) |
| Author:
|
Topolewska, Maria |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
120 |
| Issue:
|
1 |
| Year:
|
1995 |
| Pages:
|
1-12 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
rate of convergence |
| Keyword:
|
bounded variation |
| Keyword:
|
rectangular partial sums |
| Keyword:
|
double Fourier series |
| Keyword:
|
double trigonometric series |
| Keyword:
|
Borel means |
| Keyword:
|
Euler means |
| MSC:
|
42A20 |
| MSC:
|
42B05 |
| MSC:
|
42B08 |
| idZBL:
|
Zbl 0849.42009 |
| idMR:
|
MR1336942 |
| DOI:
|
10.21136/MB.1995.125893 |
| . |
| Date available:
|
2009-09-24T21:08:20Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/125893 |
| . |
| Reference:
|
[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 0572330 |
| Reference:
|
[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. MR 0713359, 10.1016/0021-9045(83)90066-7 |
| Reference:
|
[3] G. H. Hardy: Divergent series.Oxford, 1949. Zbl 0032.05801, MR 0030620 |
| Reference:
|
[4] J. Marcinkiewicz: On a class of functions and their Fourier series.Collected papers. PWN, Warszawa, 1964, pp. 36-41. |
| Reference:
|
[5] R. Taberski: On double integrals and Fourier series.Annales Polon. Math. 15 (1964), 97-115. Zbl 0171.30002, MR 0167787, 10.4064/ap-15-1-97-115 |
| Reference:
|
[6] L. Tonelli: Série Trigonometrische.Bologna, 1928. |
| Reference:
|
[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. Zbl 0625.42004, MR 0905967 |
| . |
