TY - GEN UR - http://lib.ugent.be/catalog/pug01:1260636 ID - pug01:1260636 LA - eng TI - The structure of quasiasymptotics of Schwartz distributions PY - 2010 SN - 9788386806072 SN - 0137-6934 PB - Warsaw AU - Vindas Diaz, Jasson WE01 802000645185 0000-0002-3789-8577 AU - Kamiński, Andrzej editor AU - Oberguggenberger, Michael editor AU - Pilipović, Stevan editor AB - 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. ER -Download RIS file
00000nam^a2200301^i^4500 | |||
001 | 1260636 | ||
005 | 20180813140813.0 | ||
008 | 110612s2010------------------------eng-- | ||
020 | a 9788386806072 | ||
022 | a 0137-6934 | ||
024 | a 1854/LU-1260636 2 handle | ||
024 | a 10.4064/bc88-0-24 2 doi | ||
040 | a UGent | ||
245 | a The structure of quasiasymptotics of Schwartz distributions | ||
260 | a Warsaw, Poland b Polish Academy of Sciences. Institute of Mathematics c 2010 | ||
520 | a 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. | ||
598 | a C1 | ||
100 | a Vindas Diaz, Jasson u WE01 0 802000645185 0 0000-0002-3789-8577 | ||
700 | a Kamiński, Andrzej e editor | ||
700 | a Oberguggenberger, Michael e editor | ||
700 | a Pilipović, Stevan e editor | ||
650 | a Mathematics and Statistics | ||
653 | a asymptotic behaviors of distributions | ||
653 | a quasiasymptotic behavior | ||
773 | t Linear and non-linear theory of generalized functions and its applications g Banach Center Publications. 2010. Polish Academy of Sciences. Institute of Mathematics. 88 p.297-314 q 88:<297 | ||
856 | 3 Full Text u https://biblio.ugent.be/publication/1260636/file/1264639 z [open] y BCP.pdf | ||
920 | a confcontrib | ||
Z30 | x WE 1 WE01 | ||
922 | a UGENT-WE |
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