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Abstract:

We consider smoothness properties of the generator of a principal Gabor space on the real line which is invariant under some additional translation–modulation pair. We prove that if a Gabor system on a lattice with rational density is a Riesz basis for its closed linear span, and if the closed linear span, a Gabor space, has any additional translation–modulation invariance, then its generator cannot decay well in time and in frequency simultaneously. © 2015 Elsevier Inc.

Registro:

Documento: Artículo
Título:Time–frequency shift invariance and the Amalgam Balian–Low theorem
Autor:Cabrelli, C.; Molter, U.; Pfander, G.E.
Filiación:Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón I, Buenos Aires, 1428, Argentina
IMAS/CONICET, Consejo Nacional de Investigaciones Científicas y Técnicas, Argentina
Mathematics, Jacobs University, Bremen, 28759, Germany
Mathematisch Geographische Fakultät, KU Eichstätt, Germany
Palabras clave:Additional shift invariance; Balian–Low theorem; Feichtinger algebra; Gabor frames; Time–frequency analysis; Harmonic analysis; Balian-Low theorem; Gabor frames; Gabor systems; Linear span; Riesz basis; Shift invariance; Time frequency analysis; Time-frequency shift; Modulation
Año:2016
Volumen:41
Número:3
Página de inicio:677
Página de fin:691
DOI: http://dx.doi.org/10.1016/j.acha.2015.04.003
Título revista:Applied and Computational Harmonic Analysis
Título revista abreviado:Appl Comput Harmonic Anal
ISSN:10635203
CODEN:ACOHE
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10635203_v41_n3_p677_Cabrelli

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Citas:

---------- APA ----------
Cabrelli, C., Molter, U. & Pfander, G.E. (2016) . Time–frequency shift invariance and the Amalgam Balian–Low theorem. Applied and Computational Harmonic Analysis, 41(3), 677-691.
http://dx.doi.org/10.1016/j.acha.2015.04.003
---------- CHICAGO ----------
Cabrelli, C., Molter, U., Pfander, G.E. "Time–frequency shift invariance and the Amalgam Balian–Low theorem" . Applied and Computational Harmonic Analysis 41, no. 3 (2016) : 677-691.
http://dx.doi.org/10.1016/j.acha.2015.04.003
---------- MLA ----------
Cabrelli, C., Molter, U., Pfander, G.E. "Time–frequency shift invariance and the Amalgam Balian–Low theorem" . Applied and Computational Harmonic Analysis, vol. 41, no. 3, 2016, pp. 677-691.
http://dx.doi.org/10.1016/j.acha.2015.04.003
---------- VANCOUVER ----------
Cabrelli, C., Molter, U., Pfander, G.E. Time–frequency shift invariance and the Amalgam Balian–Low theorem. Appl Comput Harmonic Anal. 2016;41(3):677-691.
http://dx.doi.org/10.1016/j.acha.2015.04.003