The structure of quasiasymptotics of Schwartz distributions

• Autorzy: Jasson Vindas
• Języki publikacji: EN

Abstrakty

EN

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 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(λx) = O(ρ(λ)) in 𝒟', where ρ is a regularly varying function.

Kategorie tematyczne

• 42A24: Summability and absolute summability of Fourier and trigonometric series
• 46F10: Operations with distributions
• 41A60: Asymptotic approximations, asymptotic expansions (steepest descent, etc.)
• 26A12: Rate of growth of functions, orders of infinity, slowly varying functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2010
• Tom: 88
• Numer: 1
• Strony: 297-314

Daty

wydano

2010

Twórcy

autor

Jasson Vindas

• Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, U.S.A.
• Department of Pure Mathematics and Computer Algebra, Ghent University, Krijgslaan 281 Gebouw S22, B 9000 Gent, Belgium

Identyfikatory

DOI

10.4064/bc88-0-24