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 \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.
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