| Title:
|
On the behavior near the origin of double sine series with monotone coefficients (English) |
| Author:
|
Krasniqi, Xhevat Z. |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
134 |
| Issue:
|
3 |
| Year:
|
2009 |
| Pages:
|
255-273 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we obtain estimates of the sum of double sine series near the origin, with monotone coefficients tending to zero. In particular (if the coefficients $a_{k,l}$ satisfy certain conditions) the following order equality is proved $$ g(x,y)\sim mna_{m,n}+\frac mn\sum _{l=1}^{n-1}la_{m,l}+\frac nm\sum _{k=1}^{m-1}ka_{k,n}+\frac 1{mn}\sum _{l=1}^{n-1}\sum _{k=1}^{m-1}kla_{k,l}, $$ where $x\in (\frac {\pi }{m+1}, \frac {\pi }m]$, $ y\in (\frac {\pi }{n+1}, \frac {\pi }n]$, $ m, n=1,2,\dots $. (English) |
| Keyword:
|
double sine series |
| Keyword:
|
sum of a double sine series with monotone coefficients |
| MSC:
|
42A16 |
| MSC:
|
42A20 |
| idZBL:
|
Zbl 1212.42006 |
| idMR:
|
MR2561305 |
| DOI:
|
10.21136/MB.2009.140660 |
| . |
| Date available:
|
2010-07-20T18:02:03Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140660 |
| . |
| 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:
|
[6] Aljančić, S., Bojanić, R., Tomić, M.: Sur le comportement asymptotique au voisinage de zéro des séries trigonométriques de sinus à coefficients monotones.Publ. Inst. Math. Acad. Serie Sci. 10 (1956), 101-120. MR 0082579 |
| Reference:
|
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| Reference:
|
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| Reference:
|
[9] Popov, A. Yu.: Estimates of the sums of sine series with monotone coefficients of certain classes.Mathematical Notes 74 (2003), 829-840. Zbl 1156.42303, MR 2054006, 10.1023/B:MATN.0000009019.66625.fb |
| Reference:
|
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| Reference:
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| Reference:
|
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| Reference:
|
[13] Vukolova, T. M., Dyachenko, M. I.: On the properties of sums of trigonometric series with monotone coefficients.Mosc. Univ. Math. Bull. (1995), 50 19-27. Zbl 0881.42004, MR 1376350 |
| . |
