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Zeitschrift für Analysis und ihre Anwendungen

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Volume 21, Issue 4, 2002, pp. 1027–1042
DOI: 10.4171/ZAA/1124

Published online: 2002-12-31

Wiener-Type Tauberian Theorems for Fourier Hyperfunctions

Stevan Pilipović[1] and Bogoljub Stanković[2]

(1) University Novi Sad, Serbia
(2) University Novi Sad, Serbia

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 $(f \star \mathcal K) (x)$ as $x \rightarrow \infty$, where $\mathcal K$ is Hörmaner’s kernel. Moreover, Wiener-type theorems are used for the asympthotic analysis of solutions to some (pseudo-)differential equations.

Keywords: Fourier hyperfunction, Tauberian theorem

Pilipović Stevan, Stanković Bogoljub: Wiener-Type Tauberian Theorems for Fourier Hyperfunctions. Z. Anal. Anwend. 21 (2002), 1027-1042. doi: 10.4171/ZAA/1124