| Title:
|
Uniform convergence of double trigonometric series (English) |
| Author:
|
Kórus, Péter |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
138 |
| Issue:
|
3 |
| Year:
|
2013 |
| Pages:
|
225-243 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
It is a classical problem in Fourier analysis to give conditions for a single sine or cosine series to be uniformly convergent. Several authors gave conditions for this problem supposing that the coefficients are monotone, non-negative or more recently, general monotone. There are also results for the regular convergence of double sine series to be uniform in case the coefficients are monotone or general monotone double sequences. In this paper we give new sufficient conditions for the uniformity of the regular convergence of sine-cosine and double cosine series, which are necessary as well in case the coefficients are non-negative. The new results also bring necessary and sufficient conditions for the uniform regular convergence of double trigonometric series in complex form. (English) |
| Keyword:
|
sine series |
| Keyword:
|
cosine series |
| Keyword:
|
double sine series |
| Keyword:
|
sine-cosine series |
| Keyword:
|
double cosine series |
| Keyword:
|
uniform convergence |
| Keyword:
|
regular convergence |
| Keyword:
|
general monotone sequence |
| Keyword:
|
general monotone double sequence |
| Keyword:
|
supremum bounded variation |
| MSC:
|
42A20 |
| MSC:
|
42A32 |
| MSC:
|
42B99 |
| idZBL:
|
Zbl 06260031 |
| idMR:
|
MR3136495 |
| DOI:
|
10.21136/MB.2013.143434 |
| . |
| Date available:
|
2013-09-14T11:45:06Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143434 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[7] Móricz, F.: Some remarks on the notion of regular convergence of multiple series.Acta Math. Hung. 41 (1983), 161-168. MR 0704536, 10.1007/BF01994074 |
| Reference:
|
[8] Tikhonov, S.: Trigonometric series with general monotone coefficients.J. Math. Anal. Appl. 326 (2007), 721-735. Zbl 1141.42004, MR 2277815, 10.1016/j.jmaa.2006.02.053 |
| Reference:
|
[9] Tikhonov, S.: Best approximation and moduli of smoothness: Computation and equivalence theorems.J. Approx. Theory 153 (2008), 19-39. Zbl 1215.42002, MR 2432551, 10.1016/j.jat.2007.05.006 |
| Reference:
|
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| Reference:
|
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| . |
