Two Wiener-type Tauberian theorems concerning Fourier hyperfunctions are proved and commented. It is shownt that the shift asymptotics (-asymptotics) of a hyperfunction is determined by the ordinary asymptotics of as , where is Hörmaner’s kernel. Moreover, Wiener-type theorems are used for the asympthotic analysis of solutions to some (pseudo-)differential equations.
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Stevan Pilipović, Bogoljub Stanković, Wiener-Type Tauberian Theorems for Fourier Hyperfunctions. Z. Anal. Anwend. 21 (2002), no. 4, pp. 1027–1042DOI 10.4171/ZAA/1124