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A Quantitative Balian-Low Theorem

Nitzan, Shahaf and Olsen, Jan-Fredrik LU (2013) In Journal of Fourier Analysis and Applications 19(5). p.1078-1092
Abstract
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.
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author
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organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Balian-Low theorem, Riesz bases, Frames, Gabor systems, Time-frequency, analysis, Uncertainty principles, Zak transform
in
Journal of Fourier Analysis and Applications
volume
19
issue
5
pages
1078 - 1092
publisher
Springer
external identifiers
  • wos:000325253900009
  • scopus:84885031805
ISSN
1531-5851
DOI
10.1007/s00041-013-9289-y
language
English
LU publication?
yes
id
231d27c8-4c90-4d71-b4a7-a26232b9dceb (old id 4172049)
date added to LUP
2016-04-01 10:48:03
date last changed
2025-10-14 10:53:46
@article{231d27c8-4c90-4d71-b4a7-a26232b9dceb,
  abstract     = {{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.}},
  author       = {{Nitzan, Shahaf and Olsen, Jan-Fredrik}},
  issn         = {{1531-5851}},
  keywords     = {{Balian-Low theorem; Riesz bases; Frames; Gabor systems; Time-frequency; analysis; Uncertainty principles; Zak transform}},
  language     = {{eng}},
  number       = {{5}},
  pages        = {{1078--1092}},
  publisher    = {{Springer}},
  series       = {{Journal of Fourier Analysis and Applications}},
  title        = {{A Quantitative Balian-Low Theorem}},
  url          = {{http://dx.doi.org/10.1007/s00041-013-9289-y}},
  doi          = {{10.1007/s00041-013-9289-y}},
  volume       = {{19}},
  year         = {{2013}},
}