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Zeros of the Wigner Distribution and the Short-Time Fourier Transform

hal.structure.identifierFakultät für Mathematik [Wien]
dc.contributor.authorGRÖCHENIG, Karlheinz
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorJAMING, Philippe
hal.structure.identifierDepartment of Mathematical Sciences
hal.structure.identifierInstitute for Advanced Study [Princeton] [IAS]
dc.contributor.authorMALINNIKOVA, Eugenia
dc.date.accessioned2024-04-04T03:04:21Z
dc.date.available2024-04-04T03:04:21Z
dc.date.issued2020
dc.identifier.issn1139-1138
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/193144
dc.description.abstractEnWe study the question under which conditions the zero set of a (cross-) Wigner distribution W (f, g) or a short-time Fourier transform is empty. This is the case when both f and g are generalized Gaussians, but we will construct less obvious examples consisting of exponential functions and their convolutions. The results require elements from the theory of totally positive functions, Bessel functions, and Hurwitz polynomials. The question of zero-free Wigner distributions is also related to Hudson's theorem for the positivity of the Wigner distribution and to Hardy's uncertainty principle. We then construct a class of step functions S so that the Wigner distribution W (f, 1 (0,1)) always possesses a zero f ∈ S ∩ L p for p < ∞, but may be zero-free for f ∈ S ∩ L ∞. The examples show that the question of zeros of the Wigner distribution may be quite subtle and relate to several branches of analysis.
dc.language.isoen
dc.publisherUniversidad Complutense
dc.title.enZeros of the Wigner Distribution and the Short-Time Fourier Transform
dc.typeArticle de revue
dc.subject.halMathématiques [math]/Analyse classique [math.CA]
dc.subject.halMathématiques [math]/Analyse fonctionnelle [math.FA]
dc.subject.halMathématiques [math]/Variables complexes [math.CV]
dc.identifier.arxiv1811.03937
bordeaux.journalRevista Matematica Complutense
bordeaux.page723-744
bordeaux.volume33
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-01915470
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01915470v1
bordeaux.COinSctx_ver=Z39.88-2004&amp;rft_val_fmt=info:ofi/fmt:kev:mtx:journal&amp;rft.jtitle=Revista%20Matematica%20Complutense&amp;rft.date=2020&amp;rft.volume=33&amp;rft.spage=723-744&amp;rft.epage=723-744&amp;rft.eissn=1139-1138&amp;rft.issn=1139-1138&amp;rft.au=GR%C3%96CHENIG,%20Karlheinz&amp;JAMING,%20Philippe&amp;MALINNIKOVA,%20Eugenia&amp;rft.genre=article


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