A Quantitative Balian-Low Theorem

Shahaf Nitzan; Jan-Fredrik Olsen

doi:10.1007/s00041-013-9289-y

A Quantitative Balian-Low Theorem

Shahaf Nitzan, Jan-Fredrik Olsen

Mathematics (Faculty of Sciences)

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	1078-1092
Journal	Journal of Fourier Analysis and Applications
Volume	19
Issue number	5
DOIs	https://doi.org/10.1007/s00041-013-9289-y
Publication status	Published - 2013

Subject classification (UKÄ)

Mathematical Sciences

Free keywords

Balian-Low theorem
Riesz bases
Frames
Gabor systems
Time-frequency
analysis
Uncertainty principles
Zak transform

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10.1007/s00041-013-9289-y

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title = "A Quantitative Balian-Low Theorem",

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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AU - Olsen, Jan-Fredrik

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N2 - 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.

AB - 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.

KW - Balian-Low theorem

KW - Riesz bases

KW - Frames

KW - Gabor systems

KW - Time-frequency

KW - analysis

KW - Uncertainty principles

KW - Zak transform

U2 - 10.1007/s00041-013-9289-y

DO - 10.1007/s00041-013-9289-y

M3 - Article

SN - 1531-5851

VL - 19

SP - 1078

EP - 1092

JO - Journal of Fourier Analysis and Applications

JF - Journal of Fourier Analysis and Applications

IS - 5

ER -

A Quantitative Balian-Low Theorem

Abstract

Subject classification (UKÄ)

Free keywords

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