The Gabor wave front set View Full Text


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Article Info

DATE

2014-04

AUTHORS

Luigi Rodino, Patrik Wahlberg

ABSTRACT

We define the Gabor wave front set WFG(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 WFG(aw(x,D)u)⊆WFG(u),u∈S′(Rd),a∈S0,00,where S0,00 denotes the Hörmander 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 Hörmander, and the S-wave front set of Coriasco and Maniccia. In particular, we prove that the Gabor wave front set and the global wave front set of Hörmander coincide. More... »

PAGES

625-655

References to SciGraph publications

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  • 2011-06. Micro-Local Analysis with Fourier Lebesgue Spaces. Part I in JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS
  • 2008. Banach Gelfand Triples for Gabor Analysis in PSEUDO-DIFFERENTIAL OPERATORS
  • 1994-11. Duality and Biorthogonality for Weyl-Heisenberg Frames in JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS
  • 1993-09. Lattice size estimates for Gabor decompositions in MONATSHEFTE FÜR MATHEMATIK
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  • 2010. Global Pseudo-Differential Calculus on Euclidean Spaces in NONE
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s00605-013-0592-0

    DOI

    http://dx.doi.org/10.1007/s00605-013-0592-0

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1015881682


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