Zak Transform and non-uniqueness in an extension of Pauli's phase retrieval problem
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | ANDREYS, Simon | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | JAMING, Philippe | |
| dc.date.accessioned | 2024-04-04T03:19:27Z | |
| dc.date.available | 2024-04-04T03:19:27Z | |
| dc.date.issued | 2016 | |
| dc.identifier.issn | 0133-3852 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/194510 | |
| dc.description.abstractEn | The aim of this paper is to pursue the investigation of the phase retrieval problem for the fractional Fourier transform $\ff_\alpha$started by the second author.We here extend a method of A.E.J.M Janssen toshow that there is a countable set $\qq$ such that for every finite subset $\aa\subset \qq$, there exist twofunctions $f,g$ not multiple of one an other such that $|\ff_\alpha f|=|\ff_\alpha g|$ for every $\alpha\in \aa$.Equivalently, in quantum mechanics, this result reformulates as follows:if $Q_\alpha=Q\cos\alpha+P\sin\alpha$ ($Q,P$ be the position and momentum observables),then $\{Q_\alpha,\alpha\in\aa\}$ is not informationally complete with respect to pure states.This is done by constructing two functions $\ffi,\psi$ such that $\ff_\alpha\ffi$ and $\ff_\alpha\psi$ have disjoint support for each $\alpha\in \aa$. To do so, we establish a link between $\ff_\alpha[f]$, $\alpha\in \qq$ and the Zak transform $Z[f]$generalizing the well known marginal properties of $Z$. | |
| dc.description.sponsorship | Conséquences à long terme de l'exposition péripubertaire aux cannabinoides: étude comportementale et transcriptionnelle chez le rat et analyse moléculaire chez l'homme - ANR-06-NEUR-0044 | |
| dc.language.iso | en | |
| dc.publisher | Springer Verlag | |
| dc.subject.en | Zak transform | |
| dc.subject.en | Weyl-Heisenberg transform | |
| dc.subject.en | Fractional Fourier Transform | |
| dc.subject.en | Pauli problem | |
| dc.subject.en | Phase Retrieval | |
| dc.title.en | Zak Transform and non-uniqueness in an extension of Pauli's phase retrieval problem | |
| dc.type | Article de revue | |
| dc.subject.hal | Mathématiques [math]/Analyse classique [math.CA] | |
| dc.subject.hal | Mathématiques [math]/Physique mathématique [math-ph] | |
| dc.subject.hal | Mathématiques [math]/Théorie de l'information et codage [math.IT] | |
| dc.subject.hal | Mathématiques [math]/Analyse fonctionnelle [math.FA] | |
| dc.subject.hal | Mathématiques [math]/Variables complexes [math.CV] | |
| dc.identifier.arxiv | 1501.03905 | |
| bordeaux.journal | Analysis Mathematica | |
| bordeaux.page | 185-201 | |
| bordeaux.volume | 42 | |
| 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-01103583 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01103583v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Analysis%20Mathematica&rft.date=2016&rft.volume=42&rft.spage=185-201&rft.epage=185-201&rft.eissn=0133-3852&rft.issn=0133-3852&rft.au=ANDREYS,%20Simon&JAMING,%20Philippe&rft.genre=article |
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