Uncertainty principles for integral operators
| hal.structure.identifier | Mathématiques - Analyse, Probabilités, Modélisation - Orléans [MAPMO] | |
| hal.structure.identifier | Analyse harmonique et fonctions spéciales | |
| dc.contributor.author | GHOBBER, Saifallah | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | JAMING, Philippe | |
| dc.date.accessioned | 2024-04-04T02:25:02Z | |
| dc.date.available | 2024-04-04T02:25:02Z | |
| dc.date.created | 2012-06 | |
| dc.date.issued | 2014 | |
| dc.identifier.issn | 0039-3223 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/189856 | |
| dc.description.abstractEn | The 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.iso | en | |
| dc.publisher | Instytut Matematyczny - Polska Akademii Nauk | |
| dc.subject.en | Uncertainty principles | |
| dc.subject.en | annihilating pairs | |
| dc.subject.en | Dunkl transform | |
| dc.subject.en | Fourier-Clifford transform | |
| dc.subject.en | integral operators | |
| dc.title.en | Uncertainty principles for integral operators | |
| dc.type | Article de revue | |
| dc.subject.hal | Mathématiques [math]/Analyse classique [math.CA] | |
| dc.identifier.arxiv | 1206.1195 | |
| bordeaux.journal | Studia Mathematica | |
| bordeaux.page | 197--220 | |
| bordeaux.volume | 220 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00704805 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00704805v1 | |
| bordeaux.COinS | ctx_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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