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# The structure of quasiasymptotics of Schwartz distributions

(2010) 88. p.297-314
Author
Organization
Abstract
In this article complete characterizations of quasiasymptotic behaviors of Schwartz distributions are presented by means of structural theorems. The cases at infinity and the origin are both analyzed. Special attention is paid to the quasiasymptotic of degree -1 and it is shown how the structural theorem can be used to study Ces\{a}ro and Abel summability of trigonometric series and integrals. Further properties of quasiasymptotics at infinity are discussed, the author presents a condition over test functions which allows one to evaluate them at the quasiasymptotic, these test functions are in bigger spaces than $\mathcal{S}$. An extension of the structural theorems for quasiasymptotics is given, the author studies a structural characterization of the behavior $f(\lambda x)=O(\rho(\lambda))$ in $\mathcal{D'}$, where $\rho$ is a regularly varying function.
Keywords
asymptotic behaviors of distributions, quasiasymptotic behavior

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## Citation

Chicago
Vindas Diaz, Jasson. 2010. “The Structure of Quasiasymptotics of Schwartz Distributions.” In Banach Center Publications, ed. Andrzej Kamiński, Michael Oberguggenberger, and Stevan Pilipović, 88:297–314. Warsaw, Poland: Polish Academy of Sciences. Institute of Mathematics.
APA
Vindas Diaz, J. (2010). The structure of quasiasymptotics of Schwartz distributions. In A. Kamiński, M. Oberguggenberger, & S. Pilipović (Eds.), Banach Center Publications (Vol. 88, pp. 297–314). Presented at the Linear and non-linear Theory of Generalized Functions and Its Applications, Warsaw, Poland: Polish Academy of Sciences. Institute of Mathematics.
Vancouver
1.
Vindas Diaz J. The structure of quasiasymptotics of Schwartz distributions. In: Kamiński A, Oberguggenberger M, Pilipović S, editors. Banach Center Publications. Warsaw, Poland: Polish Academy of Sciences. Institute of Mathematics; 2010. p. 297–314.
MLA
Vindas Diaz, Jasson. “The Structure of Quasiasymptotics of Schwartz Distributions.” Banach Center Publications. Ed. Andrzej Kamiński, Michael Oberguggenberger, & Stevan Pilipović. Vol. 88. Warsaw, Poland: Polish Academy of Sciences. Institute of Mathematics, 2010. 297–314. Print.
@inproceedings{1260636,
abstract     = {In this article complete characterizations of quasiasymptotic behaviors of Schwartz distributions are presented by means of structural theorems. The cases at infinity and the origin are both analyzed. Special attention is paid to the quasiasymptotic of degree -1 and it is shown how the structural theorem can be used to study Ces\{a}ro and Abel summability of trigonometric series and integrals. Further properties of quasiasymptotics at infinity are discussed, the author presents a condition over test functions  which allows one to evaluate them at the quasiasymptotic, these test functions are in bigger spaces than $\mathcal{S}$. An extension of the structural theorems for quasiasymptotics is given, the author studies a structural characterization of the behavior $f(\lambda x)=O(\rho(\lambda))$ in $\mathcal{D'}$, where $\rho$ is a regularly varying function.},
author       = {Vindas Diaz, Jasson},
booktitle    = {Banach Center Publications},
editor       = {Kamiński, Andrzej and Oberguggenberger, Michael and Pilipović, Stevan},
isbn         = {9788386806072},
issn         = {0137-6934},
keywords     = {asymptotic behaviors of distributions,quasiasymptotic behavior},
language     = {eng},
location     = {Bedlewo, Poland},
pages        = {297--314},
publisher    = {Polish Academy of Sciences. Institute of Mathematics},
title        = {The structure of quasiasymptotics of Schwartz distributions},
url          = {http://dx.doi.org/10.4064/bc88-0-24},
volume       = {88},
year         = {2010},
}


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