A Quantitative Balian-Low Theorem
(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.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/4172049
- author
- Nitzan, Shahaf and Olsen, Jan-Fredrik LU
- organization
- publishing date
- 2013
- 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
- 2022-04-04 21:29:06
@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}}, }