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The Gabor wave front set
University of Turin.
Linnaeus University, Faculty of Technology, Department of Mathematics.
2014 (English)In: Monatshefte für Mathematik (Print), ISSN 0026-9255, E-ISSN 1436-5081, Vol. 173, no 4, p. 625-655Article in journal (Refereed) Published
Abstract [en]

We define the Gabor wave front set W F-G(u) of a tempered distribution u in terms of rapid decay of its Gabor coefficients in a conic subset of the phase space. We show the inclusion W F-G(a(w) (x, D)u) subset of W F-G(u), u is an element of l'(R-d), a is an element of S-0,0(0), where S-0,0(0) denotes the Hormander symbol class of order zero and parameter values zero. We compare our definition with other definitions in the literature, namely the classical and the global wave front sets of Hormander, and the l-wave front set of Coriasco and Maniccia. In particular, we prove that the Gabor wave front set and the global wave front set of Hormander coincide.

Place, publisher, year, edition, pages
2014. Vol. 173, no 4, p. 625-655
National Category
Mathematical Analysis
Research subject
Mathematics, Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-32273DOI: 10.1007/s00605-013-0592-0ISI: 000333161400011Scopus ID: 2-s2.0-84896393828OAI: oai:DiVA.org:lnu-32273DiVA, id: diva2:695937
Available from: 2014-02-12 Created: 2014-02-12 Last updated: 2017-12-06Bibliographically approved

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Wahlberg, Patrik

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  • Other locale
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