untitled
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<identifier>oai:HAL:hal-00190006v1</identifier>
<datestamp>2017-12-21</datestamp>
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<setSpec>subject:math</setSpec>
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<metadata><dc>
<publisher>HAL CCSD</publisher>
<title lang=en>Regularity, Local and Microlocal Analysis in Theories of Generalized Functions</title>
<creator>Marti, Jean-André</creator>
<contributor>Groupe de Technologie des Surfaces et Interfaces (GTSI) ; Université des Antilles et de la Guyane (UAG) - Université des Antilles (Pôle Guadeloupe) ; Université des Antilles (UA) - Université des Antilles (UA)</contributor>
<identifier>hal-00190006</identifier>
<identifier>https://hal.archives-ouvertes.fr/hal-00190006</identifier>
<identifier>https://hal.archives-ouvertes.fr/hal-00190006/document</identifier>
<identifier>https://hal.archives-ouvertes.fr/hal-00190006/file/Regularity-Local-Microlocal-Analysis5.pdf</identifier>
<source>https://hal.archives-ouvertes.fr/hal-00190006</source>
<source>2007</source>
<identifier>ARXIV : 0711.3688</identifier>
<relation>info:eu-repo/semantics/altIdentifier/arxiv/0711.3688</relation>
<language>en</language>
<subject lang=en>Spaces and algebras of generalized functions</subject>
<subject lang=en>sheaf theory</subject>
<subject lang=en>localization</subject>
<subject lang=en>microlocalization</subject>
<subject lang=en>propagation of singularities</subject>
<subject lang=en>nonlinear PDE</subject>
<subject>35D10,46F05,46F30,46M20</subject>
<subject>[MATH.MATH-FA] Mathematics [math]/Functional Analysis [math.FA]</subject>
<type>info:eu-repo/semantics/preprint</type>
<type>Preprints, Working Papers, ...</type>
<description lang=en>We introduce a general context involving a presheaf A and a subpresheaf B of A. We show that all previously considered cases of local analysis of generalized functions (defined from duality or algebraic techniques) can be interpretated as the B-local analysis of sections of A. But the microlocal analysis of the sections of sheaves or presheaves under consideration is dissociated into a "frequential microlocal analysis " and into a "microlocal asymptotic analysis". The frequential microlocal analysis based on the Fourier transform leads to the study of propagation of singularities under only linear (including pseudodifferential) operators in the theories described here, but has been extended to some non linear cases in classical theories involving Sobolev techniques. The microlocal asymptotic analysis can inherit from the algebraic structure of B some good properties with respect to nonlinear operations.</description>
<date>2007-11-22</date>
<rights>info:eu-repo/semantics/OpenAccess</rights>
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