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The wave front set of the Wigner distribution and instantaneous frequency
Univ Turin, Dept Math, I-10123 Turin, TO, Italy.
Univ Turin, Dept Math, I-10123 Turin, TO, Italy.
Univ Turin, Dept Math, I-10123 Turin, TO, Italy.
2012 (English)In: Journal of Fourier Analysis and Applications, ISSN 1069-5869, E-ISSN 1531-5851, Vol. 18, no 2, 410-438 p.Article in journal (Refereed) Published
Abstract [en]

We prove a formula expressing the gradient of the phase function of a function f : R-d bar right arrow C as a normalized first frequency momentof the Wigner distribution for fixed time. The formula holds when f is the Fourier transform of a distribution of compact support, or when f belongs to a Sobolev space Hd/2+1+epsilon(R-d) where epsilon > 0. The restriction of the Wigner distribution to fixed time is well defined provided a certain condition on its wave front set is satisfied. Therefore we first need to study the wave front set of the Wigner distribution of a tempered distribution.

Place, publisher, year, edition, pages
Boston: Birkhäuser Verlag, 2012. Vol. 18, no 2, 410-438 p.
National Category
Mathematical Analysis
Research subject
Mathematics, Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-27575DOI: 10.1007/s00041-011-9201-6ISI: 000304148700010OAI: oai:DiVA.org:lnu-27575DiVA: diva2:637379
Available from: 2013-07-17 Created: 2013-07-17 Last updated: 2017-12-06Bibliographically approved

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Wahlberg, Patrik

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  • nn-NB
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  • Other locale
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