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Uncertainty principles for integral operators

hal.structure.identifierMathématiques - Analyse, Probabilités, Modélisation - Orléans [MAPMO]
hal.structure.identifierAnalyse harmonique et fonctions spéciales
dc.contributor.authorGHOBBER, Saifallah
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorJAMING, Philippe
dc.date.accessioned2024-04-04T02:25:02Z
dc.date.available2024-04-04T02:25:02Z
dc.date.created2012-06
dc.date.issued2014
dc.identifier.issn0039-3223
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/189856
dc.description.abstractEnThe aim of this paper is to prove new uncertainty principles for an integral operator $\tt$ with a bounded kernel for which there is a Plancherel theorem. The first of these results is an extension of Faris's local uncertainty principle which states that if a nonzero function $f\in L^2(\R^d,\mu)$ is highly localized near a single point then $\tt (f)$ cannot be concentrated in a set of finite measure. The second result extends the Benedicks-Amrein-Berthier uncertainty principle and states that a nonzero function $f\in L^2(\R^d,\mu)$ and its integral transform $\tt (f)$ cannot both have support of finite measure. From these two results we deduce a global uncertainty principle of Heisenberg type for the transformation $\tt$. We apply our results to obtain a new uncertainty principles for the Dunkl and Clifford Fourier transforms.
dc.language.isoen
dc.publisherInstytut Matematyczny - Polska Akademii Nauk
dc.subject.enUncertainty principles
dc.subject.enannihilating pairs
dc.subject.enDunkl transform
dc.subject.enFourier-Clifford transform
dc.subject.enintegral operators
dc.title.enUncertainty principles for integral operators
dc.typeArticle de revue
dc.subject.halMathématiques [math]/Analyse classique [math.CA]
dc.identifier.arxiv1206.1195
bordeaux.journalStudia Mathematica
bordeaux.page197--220
bordeaux.volume220
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-00704805
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00704805v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Studia%20Mathematica&rft.date=2014&rft.volume=220&rft.spage=197--220&rft.epage=197--220&rft.eissn=0039-3223&rft.issn=0039-3223&rft.au=GHOBBER,%20Saifallah&JAMING,%20Philippe&rft.genre=article


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