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Distributional versions of Littlewood's Tauberian theorem

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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.
Keywords
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

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Please use this url to cite or link to this publication:

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.
@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},
}

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