JournalszaaVol. 21, No. 4pp. 1027–1042

Wiener-Type Tauberian Theorems for Fourier Hyperfunctions

  • Stevan Pilipović

    University Novi Sad, Serbia
  • Bogoljub Stanković

    University Novi Sad, Serbia
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Abstract

Two Wiener-type Tauberian theorems concerning Fourier hyperfunctions are proved and commented. It is shownt that the shift asymptotics (SS-asymptotics) of a hyperfunction ff is determined by the ordinary asymptotics of (fK)(x)(f \star \mathcal K) (x) as xx \rightarrow \infty, where K\mathcal K is Hörmaner’s kernel. Moreover, Wiener-type theorems are used for the asympthotic analysis of solutions to some (pseudo-)differential equations.

Cite this article

Stevan Pilipović, Bogoljub Stanković, Wiener-Type Tauberian Theorems for Fourier Hyperfunctions. Z. Anal. Anwend. 21 (2002), no. 4, pp. 1027–1042

DOI 10.4171/ZAA/1124