A Quantitative Balian-Low Theorem

Summary, in English

We study functions generating Gabor Riesz bases on the integer lattice. The classical Balian-Low theorem (BLT) restricts the simultaneous time and frequency localization of such functions. We obtain a quantitative estimate on their Zak transform that extends both this result and the more general (p,q) Balian-Low theorem. Moreover, we establish a family of quantitative amalgam-type Balian-Low theorems that contain both the amalgam BLT and the classical BLT as special cases.

• Författare: Shahaf Nitzan; Jan-Fredrik Olsen
• Avdelning/ar: Matematik (naturvetenskapliga fakulteten)
• Publiceringsår: 2013
• Språk: Engelska
• Sidor: 1078-1092
• Publikation/Tidskrift/Serie: Journal of Fourier Analysis and Applications
• Volym: 19
• Issue: 5
• Länkar: http://dx.doi.org/10.1007/s00041-013-9289-y
• Dokumenttyp: Artikel i tidskrift
• Förlag: Springer
• Ämne: Mathematics
• Nyckelord: Balian-Low theorem; Riesz bases; Frames; Gabor systems; Time-frequency; analysis; Uncertainty principles; Zak transform
• Status: Published
• ISBN/ISSN/Övrigt: ISSN: 1531-5851