EMIS ELibM Electronic Journals Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques
Vol. CXXII, No. 26, pp. 75–105 (2001)

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On the microlocal decomposition of ultradistributions and ultradifferentiable functions

A. Eida

Faculty of Engineering Science, Tokyo University of Technology, 1404-1 Katakura, Hachioji, Tokyo 192-8580, JAPAN, eida@cc.teu.ac.jp

Abstract: The microlocal decomposition for ultradistributions and ultradifferentiable functions is derived by Bengel-Schapira's method and these classes of functions are microlocalized as subsheaves $\FC_M^*$, $\FC_M^{d,*}$ of the sheaf $\FC_M$ of Sato's microfunctions on a real analytic manifold $M$. Moreover, the exactness of the sequences $$\sexact{\FA_M}{\FDB^*_M}{\pi_*\FC^*_M}$$ and $$\sexact{\FA_M}{\FDF^*_M}{\pi_*\FC_M^{d,*}}$$ is shown and some fundamental properties on $\FC_M^*$, $\FC_M^{d,*}$ are described. Here $\FDB^*_M$ is a sheaf of ultradistributions and $\FDF^*_M$ is a sheaf of ultradifferentiable functions. We give some solvability conditions applicable to partial differential equations by operating Aoki's classes of microdifferential operators of infinite order on these sheaves.

Keywords: hyperfunctions, ultradistributions, ultradifferentiable functions, microdifferential operators

Classification (MSC2000): 58J15

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Electronic fulltext finalized on: 20 Aug 2001. This page was last modified: 20 Jun 2011.

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