Time-frequency shift invariance and the Amalgam Balian-Low theorem

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• 作者：Carlos Cabrelli^a ; ^b ; ^{cabrelli@dm.uba.ar" class="auth_mail" title="E-mail the corresponding author} ; Ursula Molter^a ; ^b ; ^{umolter@dm.uba.ar" class="auth_mail" title="E-mail the corresponding author} ; Gö ; tz E. Pfander^c ; ^d ; ^{g.pfander@jacobs-university.de" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Balian&ndash ; Low theorem ; Additional shift invariance ; Gabor frames ; Time&ndash ; frequency analysis ; Feichtinger algebra
• 刊名：Applied and Computational Harmonic Analysis
• 出版年：2016
• 出版时间：November 2016
• 年：2016
• 卷：41
• 期：3
• 页码：677-691
• 全文大小：476 K

文摘

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.