Wiener-Type Tauberian Theorems for Fourier Hyperfunctions

Abstract

Two Wiener-type Tauberian theorems concerning Fourier hyperfunctions are proved and commented. It is shownt that the shift asymptotics (S-asymptotics) of a hyperfunction f is determined by the ordinary asymptotics of (f * K)(x) as x → ∞, where K is Hörmaner's kernel. Moreover, Wiener-type theorems are used for the asympthotic analysis of solutions to some (pseudo-)differential equations.