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dc.contributor.author
Antezana, Jorge Abel
dc.contributor.author
Bruna, Joaquim
dc.contributor.author
Pujals, Enrique
dc.date.available
2021-08-27T02:58:53Z
dc.date.issued
2020-07-24
dc.identifier.citation
Antezana, Jorge Abel; Bruna, Joaquim; Pujals, Enrique; Linear independence of time–frequency translates in Lp spaces; Birkhauser Boston Inc; Journal Of Fourier Analysis And Applications; 26; 63; 24-7-2020; 1-15
dc.identifier.issn
1069-5869
dc.identifier.uri
http://hdl.handle.net/11336/139058
dc.description.abstract
We study the Heil-Ramanathan-Topiwala conjecture in L^p spaces by reformulating it as a fixed point problem. This reformulation shows that a function with linearly dependent time-frequency translates has a very rigid structure, which is encoded in a family of linear operators. This is used to give an elementary proof that if f∈ L^p(R) , p∈ [ 1 , 2 ] , and Λ ⊆ R× R is contained in a lattice then the set of time frequency translates (f(a,b))(a,b)∈Λ is linearly independent. Our proof also works for the case 2 < p< ∞ if Λ is contained in a lattice of the form αZ× βZ.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
Birkhauser Boston Inc
dc.rights
info:eu-repo/semantics/restrictedAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
TIME FREQUENCY TRANSLATES
dc.subject
LINEAR INDEPENDENCE
dc.subject
ERGODICITY
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SYMPLECTIC TRANSFORMATION
dc.subject
LATTICE
dc.subject
LP SPACES
dc.subject.classification
Matemática Pura
dc.subject.classification
Matemáticas
dc.subject.classification
CIENCIAS NATURALES Y EXACTAS
dc.title
Linear independence of time–frequency translates in Lp spaces
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2021-08-19T20:30:21Z
dc.journal.volume
26
dc.journal.number
63
dc.journal.pagination
1-15
dc.journal.pais
Estados Unidos
dc.description.fil
Fil: Antezana, Jorge Abel. Universidad Nacional de La Plata; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
dc.description.fil
Fil: Bruna, Joaquim. Universitat Autònoma de Barcelona; España
dc.description.fil
Fil: Pujals, Enrique. City University of New York; Estados Unidos
dc.journal.title
Journal Of Fourier Analysis And Applications
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.1007/s00041-020-09774-2
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs00041-020-09774-2
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