Extension of Sato's hyperfunctions

Michael Langenbruch

doi:10.7169/facm/1301497745

March 2011 Extension of Sato's hyperfunctions

Michael Langenbruch

Funct. Approx. Comment. Math. 44(1): 33-44 (March 2011). DOI: 10.7169/facm/1301497745

Abstract

We characterize possible bounds for representing functions of arbitrary hyperfunctions. Specifically, there are always representing functions decreasing rapidly outside each strip near $\mathbb{R}$. Also, exponential decrease of any type on any strip $\mathbb{R}\times \pm i[c,C], 0<c<C<\infty,$ can be achieved. This will be used in [10] to define an asymptotic Fourier and Laplace transformation on the space of hyperfunctions.

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Michael Langenbruch "Extension of Sato's hyperfunctions," Functiones et Approximatio Commentarii Mathematici 44(1), 33-44, (March 2011). https://doi.org/10.7169/facm/1301497745

Published: March 2011

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