THE CRAMER-WOLD THEOREM ON QUADRATIC SURFACES AND HEISENBERG UNIQUENESS PAIRS
| hal.structure.identifier | Fakultät für Mathematik [Wien] | |
| dc.contributor.author | GRÖCHENIG, Karlheinz | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | JAMING, Philippe | |
| dc.date.accessioned | 2024-04-04T03:14:07Z | |
| dc.date.available | 2024-04-04T03:14:07Z | |
| dc.date.issued | 2020 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/194016 | |
| dc.description.abstractEn | Two measurable sets S, Λ ⊆ R d form a Heisenberg uniqueness pair, if every bounded measure µ with support in S whose Fourier transform vanishes on Λ must be zero. We show that a quadratic hypersurface and the union of two hyperplanes in general position form a Heisenberg uniqueness pair in R d. As a corollary we obtain a new, surprising version of the classical Cramér-Wold theorem: a bounded measure supported on a quadratic hypersurface is uniquely determined by its projections onto two generic hyperplanes (whereas an arbitrary measure requires the knowledge of a dense set of projections). We also give an application to the unique continuation of eigenfunctions of second-order PDEs with constant coefficients . | |
| dc.description.sponsorship | Géométrie des mesures convexes et discrètes - ANR-11-BS01-0007 | |
| dc.description.sponsorship | Analyse Variationnelle en Tomographies photoacoustique, thermoacoustique et ultrasonore - ANR-12-BS01-0001 | |
| dc.description.sponsorship | Initiative d'excellence de l'Université de Bordeaux - ANR-10-IDEX-0003 | |
| dc.language.iso | en | |
| dc.subject.en | Heisenberg Uniqueness | |
| dc.subject.en | Cramer-Wold theorem | |
| dc.subject.en | Unique continuation | |
| dc.title.en | THE CRAMER-WOLD THEOREM ON QUADRATIC SURFACES AND HEISENBERG UNIQUENESS PAIRS | |
| dc.type | Article de revue | |
| dc.subject.hal | Mathématiques [math]/Analyse classique [math.CA] | |
| dc.subject.hal | Mathématiques [math]/Analyse fonctionnelle [math.FA] | |
| dc.subject.hal | Mathématiques [math]/Variables complexes [math.CV] | |
| dc.subject.hal | Mathématiques [math]/Probabilités [math.PR] | |
| dc.subject.hal | Mathématiques [math]/Equations aux dérivées partielles [math.AP] | |
| dc.identifier.arxiv | 1608.06738 | |
| bordeaux.journal | Journal de l'Institut de Mathématiques de Jussieu | |
| bordeaux.page | 117-135 | |
| bordeaux.volume | 19 | |
| 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-01355577 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01355577v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Journal%20de%20l'Institut%20de%20Math%C3%A9matiques%20de%20Jussieu&rft.date=2020&rft.volume=19&rft.spage=117-135&rft.epage=117-135&rft.au=GR%C3%96CHENIG,%20Karlheinz&JAMING,%20Philippe&rft.genre=article |
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