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## The structure of quasiasymptotics of Schwartz distributions

### Volume 88 / 2010

Banach Center Publications 88 (2010), 297-314 MSC: Primary 46F10, 41A60; Secondary 26A12, 42A24. DOI: 10.4064/bc88-0-24

#### Abstract

In this article complete characterizations of the quasiasymptotic behavior 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 quasiasymptotics of degree $-1$. It is shown how the structural theorem can be used to study Cesàro and Abel summability of trigonometric series and integrals. Further properties of quasiasymptotics at infinity are discussed. A condition for test functions in bigger spaces than $\mathcal{S}$ is presented which allows one to consider the respective quasiasymptotics over them. 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.

#### Authors

• Jasson VindasDepartment of Mathematics
Louisiana State University
Baton Rouge, LA 70803, U.S.A.