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Carleman regularization in theC∞

Carleman regularization in theC∞ Ann. Univ. Ferrara - Sez. VII - Sc. Mat. Suppl. Vol. XLV, 213-240 (1999) Carleman Regularization in the C~-Category. OTTO LIESS (*) To the memory of L. Cattabriga 1. - Introduction. The present paper is an attempt to explain a number of classical facts in the theory of e~-microlocalization with arguments normally associated with mi- crolocal analysis in the analytic category. In particular, we shall develop a the- ory of the Fourier-(inverse) transform in distributions which is parallel to the theory developed for hyperfunctions in [11], [12]. Here we recall that in the analytic category microlocal arguments can be based on two rather different points of view. One is geometrical and has found its realization in what is sometimes called algebraic analysis. It was initiated by M. Sato and relies heavily on sheaf-theoretic and cohomological methods. The other point of view was introduced by HSrmander and relies mainly on the theory of the Fourier- transform. The fact that in analytic microlocalization the two points of view are equivalent is Bony's theorem (cf. [2]) and the relation between them has been analyzed in a systematic way. One of the most efficient tools developed in or- der to understand this relation http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ANNALI DELL UNIVERSITA DI FERRARA Springer Journals

Carleman regularization in theC∞

Liess, Otto
ANNALI DELL UNIVERSITA DI FERRARA , Volume 45 (1) – Jan 1, 1999
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References (12)

Publisher
Springer Journals
Copyright
Copyright © Università degli Studi di Ferrara 1999
ISSN
0430-3202
eISSN
1827-1510
DOI
10.1007/bf02826096
Publisher site
See Article on Publisher Site

Abstract

Ann. Univ. Ferrara - Sez. VII - Sc. Mat. Suppl. Vol. XLV, 213-240 (1999) Carleman Regularization in the C~-Category. OTTO LIESS (*) To the memory of L. Cattabriga 1. - Introduction. The present paper is an attempt to explain a number of classical facts in the theory of e~-microlocalization with arguments normally associated with mi- crolocal analysis in the analytic category. In particular, we shall develop a the- ory of the Fourier-(inverse) transform in distributions which is parallel to the theory developed for hyperfunctions in [11], [12]. Here we recall that in the analytic category microlocal arguments can be based on two rather different points of view. One is geometrical and has found its realization in what is sometimes called algebraic analysis. It was initiated by M. Sato and relies heavily on sheaf-theoretic and cohomological methods. The other point of view was introduced by HSrmander and relies mainly on the theory of the Fourier- transform. The fact that in analytic microlocalization the two points of view are equivalent is Bony's theorem (cf. [2]) and the relation between them has been analyzed in a systematic way. One of the most efficient tools developed in or- der to understand this relation

Journal

ANNALI DELL UNIVERSITA DI FERRARA – Springer Journals

Published: Jan 1, 1999

Keywords: Analytic Function; Pseudodifferential Operator; Open Cone; Plurisubharmonic Function; Oscillatory Integral

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