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dc.contributor.author
Wellershoff, Matthias
dc.date.accessioned
2023-09-05T13:58:36Z
dc.date.available
2023-08-30T10:34:08Z
dc.date.available
2023-09-05T13:58:36Z
dc.date.issued
2024-02-15
dc.identifier.issn
0022-247X
dc.identifier.issn
1096-0813
dc.identifier.other
10.1016/j.jmaa.2023.127692
en_US
dc.identifier.uri
http://hdl.handle.net/20.500.11850/628960
dc.description.abstract
It was recently shown that functions in L4([−B,B]) can be uniquely recovered up to a global phase factor from the absolute values of their Gabor transforms sampled on a rectangular lattice. We prove that this remains true if one replaces L4([−B,B]) by Lp([−B,B]) with p∈[1,∞]. To do so, we adapt the original proof by Grohs and Liehr and use a classical sampling result due to Beurling. Furthermore, we present a minor modification of a result of Müntz–Szász type by Zalik. Finally, we consider the implications of our results for more general function spaces obtained by applying the fractional Fourier transform to Lp([−B,B]) and for more general nonuniform sampling sets.
en_US
dc.language.iso
en
en_US
dc.publisher
Elsevier
en_US
dc.subject
Phase retrieval
en_US
dc.subject
Gabor transform
en_US
dc.subject
Sampling theory
en_US
dc.subject
Time-frequency analysis
en_US
dc.title
Injectivity of sampled Gabor phase retrieval in spaces with general integrability conditions
en_US
dc.type
Journal Article
dc.date.published
2023-08-21
ethz.journal.title
Journal of Mathematical Analysis and Applications
ethz.journal.volume
530
en_US
ethz.journal.issue
2
en_US
ethz.journal.abbreviated
J. math. anal. appl.
ethz.pages.start
127692
en_US
ethz.size
10 p.
en_US
ethz.grant
Mathematical analysis of the phase retrieval problem
en_US
ethz.publication.place
Amsterdam
en_US
ethz.publication.status
published
en_US
ethz.leitzahl
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02501 - Seminar für Angewandte Mathematik / Seminar for Applied Mathematics::09603 - Alaifari, Rima / Alaifari, Rima
en_US
ethz.leitzahl.certified
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02501 - Seminar für Angewandte Mathematik / Seminar for Applied Mathematics::09603 - Alaifari, Rima / Alaifari, Rima
en_US
ethz.grant.agreementno
184698
ethz.grant.fundername
SNF
ethz.grant.funderDoi
10.13039/501100001711
ethz.grant.program
Projekte MINT
ethz.relation.isNewVersionOf
20.500.11850/521790
ethz.date.deposited
2023-08-30T10:34:08Z
ethz.source
FORM
ethz.eth
yes
en_US
ethz.availability
Metadata only
en_US
ethz.rosetta.installDate
2023-09-05T13:58:39Z
ethz.rosetta.lastUpdated
2024-02-03T03:18:08Z
ethz.rosetta.versionExported
true
ethz.COinS
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