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Distributional versions of Littlewood's Tauberian theorem

Ricardo Estrada and Jasson Vindas Diaz UGent (2013) CZECHOSLOVAK MATHEMATICAL JOURNAL. 63(2). p.403-420
abstract
We provide several general versions of Littlewood's Tauberian theorem. These versions are applicable to Laplace transforms of Schwartz distributions. We apply these Tauberian results to deduce a number of Tauberian theorems for power series where Cesaro 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.
Please use this url to cite or link to this publication:
author
organization
year
type
journalArticle (original)
publication status
published
subject
keyword
Laplace transform, Tauberian theorems, The converse of Abel’s theorem, Littlewood’s Tauberian theorem, Abel and Cesaro summability, Distributional Tauberian theorems, Asymptotic behavior of generalized functions, DIRICHLETS SERIES, POWER-SERIES, SUMMABILITY, BEHAVIOR, CONVERSE
journal title
CZECHOSLOVAK MATHEMATICAL JOURNAL
Czech. Math. J.
volume
63
issue
2
pages
403 - 420
Web of Science type
Article
Web of Science id
000321762100006
JCR category
MATHEMATICS
JCR impact factor
0.294 (2013)
JCR rank
273/302 (2013)
JCR quartile
4 (2013)
ISSN
0011-4642
DOI
10.1007/s10587-013-0025-1
language
English
UGent publication?
yes
classification
A1
copyright statement
I have transferred the copyright for this publication to the publisher
id
4115871
handle
http://hdl.handle.net/1854/LU-4115871
date created
2013-08-14 13:31:38
date last changed
2016-12-19 15:46:03
@article{4115871,
  abstract     = {We provide several general versions of Littlewood's Tauberian theorem. These versions are applicable to Laplace transforms of Schwartz distributions. We apply these Tauberian results to deduce a number of Tauberian theorems for power series where Cesaro 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.},
  author       = {Estrada, Ricardo and Vindas Diaz, Jasson},
  issn         = {0011-4642},
  journal      = {CZECHOSLOVAK MATHEMATICAL JOURNAL},
  keyword      = {Laplace transform,Tauberian theorems,The converse of Abel{\textquoteright}s theorem,Littlewood{\textquoteright}s Tauberian theorem,Abel and Cesaro summability,Distributional Tauberian theorems,Asymptotic behavior of generalized functions,DIRICHLETS SERIES,POWER-SERIES,SUMMABILITY,BEHAVIOR,CONVERSE},
  language     = {eng},
  number       = {2},
  pages        = {403--420},
  title        = {Distributional versions of Littlewood's Tauberian theorem},
  url          = {http://dx.doi.org/10.1007/s10587-013-0025-1},
  volume       = {63},
  year         = {2013},
}

Chicago
Estrada, Ricardo, and Jasson Vindas Diaz. 2013. “Distributional Versions of Littlewood’s Tauberian Theorem.” Czechoslovak Mathematical Journal 63 (2): 403–420.
APA
Estrada, R., & Vindas Diaz, J. (2013). Distributional versions of Littlewood’s Tauberian theorem. CZECHOSLOVAK MATHEMATICAL JOURNAL, 63(2), 403–420.
Vancouver
1.
Estrada R, Vindas Diaz J. Distributional versions of Littlewood’s Tauberian theorem. CZECHOSLOVAK MATHEMATICAL JOURNAL. 2013;63(2):403–20.
MLA
Estrada, Ricardo, and Jasson Vindas Diaz. “Distributional Versions of Littlewood’s Tauberian Theorem.” CZECHOSLOVAK MATHEMATICAL JOURNAL 63.2 (2013): 403–420. Print.