| Title:
|
Distributional versions of Littlewood's Tauberian theorem (English) |
| Author:
|
Estrada, Ricardo |
| Author:
|
Vindas, Jasson |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
63 |
| Issue:
|
2 |
| Year:
|
2013 |
| Pages:
|
403-420 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We provide several general versions of Littlewood's Tauberian theorem. These versions are applicable to Laplace transforms of Schwartz distributions. We employ two types of Tauberian hypotheses; the first kind involves distributional boundedness, while the second type imposes a one-sided assumption on the Cesàro behavior of the distribution. We apply these Tauberian results to deduce a number of Tauberian theorems for power series and Stieltjes integrals where Cesàro summability follows from Abel summability. We also use our general results to give a new simple proof of the classical Littlewood one-sided Tauberian theorem for power series. (English) |
| Keyword:
|
Tauberian theorem |
| Keyword:
|
Laplace transform |
| Keyword:
|
the converse of Abel's theorem |
| Keyword:
|
Littlewood's Tauberian theorem |
| Keyword:
|
Abel and Cesàro summability |
| Keyword:
|
distributional Tauberian theorem |
| Keyword:
|
asymptotic behavior of generalized function |
| MSC:
|
40E05 |
| MSC:
|
40G05 |
| MSC:
|
40G10 |
| MSC:
|
44A10 |
| MSC:
|
46F12 |
| MSC:
|
46F20 |
| idZBL:
|
Zbl 06236419 |
| idMR:
|
MR3073966 |
| DOI:
|
10.1007/s10587-013-0025-1 |
| . |
| Date available:
|
2013-07-18T14:56:16Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143320 |
| . |
| Reference:
|
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