Necessary and sufficient conditions for the local solvability in hyperfunctions of a class of systems of complex vector fields
type: Item
instance of: scholarly article
title: Necessary and sufficient conditions for the local solvability in hyperfunctions of a class of systems of complex vector fields
zbMATH Open document ID: 0834.35004
DOI: 10.1007/BF01241132
author: Paulo D. Cordaro
author: François Treves
published in: Inventiones Mathematicae
publication date: 1995-08-13T00:00:00Z
full work available at URL: https://eudml.org/doc/144279
review text: A necessary and sufficient condition is proved for the local exactness at degree \(q\geq 1\) of the differential complex attached to a locally integrable structure of codimension one, in spaces of hyperfunctions with respect to the hypo-analytic structure associated to a smooth ``first integral'' \(Z\) on a general smooth manifold (cf. [\textit{F. Treves}, Hypo- analytic structures: local theory. Princeton Mathematical Series. Princeton, NJ: Princeton University Press (1992; Zbl 0787.35003)]). The condition is that the singular homology of the fibres of the map \(Z\) be trivial in dimension \(q-1\). This is considered to be an analogue of the Poincaré lemma for the present situation, but the true content is a kind of local solvability for some systems of vector fields with complex coefficients.
Mathematics Subject Classification ID: 35A07
Mathematics Subject Classification ID: 58J15
Mathematics Subject Classification ID: 32C38
Mathematics Subject Classification ID: 58J10
Mathematics Subject Classification ID: 32C35
Mathematics Subject Classification ID: 32V05
Mathematics Subject Classification ID: 35A27
Mathematics Subject Classification ID: 35F05
zbMATH DE Number: 784005
zbMATH Keywords: hypo-analytic structure
zbMATH Keywords: Poincaré lemma
reviewed by: Akira Kaneko
MaRDI profile type: Publication
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OpenAlex ID: W2025822366
description: scientific article; zbMATH DE number 784005