Linear independence of finite Gabor systems determined by behavior at infinity

DOI10.1007/s12220-013-9423-8zbMath1311.42073arXiv1211.0337OpenAlexW2117813496MaRDI QIDQ2256830

Abdelkrim Bourouihiya, John J. Benedetto

Publication date: 23 February 2015

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1211.0337

zbMATH Keywords

Kronecker's theoremGabor systemsHardy fieldsHRT conjecture

Mathematics Subject Classification ID

General harmonic expansions, frames (42C15) Completeness of sets of functions in nontrigonometric harmonic analysis (42C30)

Related Items (7)

Linear independence of time-frequency translates in \(\mathbb R^d\) ⋮ The HRT Conjecture and the Zero Divisor Conjecture for the Heisenberg Group ⋮ Linear independence of a finite set of time-frequency shifts ⋮ Translates of Functions on the Heisenberg Group and the HRT Conjecture ⋮ Letter to the editor: proof of the HRT conjecture for almost every \((1,3)\) configuration ⋮ Extension and restriction principles for the HRT conjecture ⋮ Letter to the editor: linear independence of time-frequency shifts up to extreme dilations

Cites Work

• Linear independence of Parseval wavelets
• Proof of the HRT conjecture for configurations
• Diophantine approximation
• Differentiably finite power series
• Linear independence of time-frequency shifts under a generalized Schrödinger representation
• Valuation theory of exponential Hardy fields. I
• Foundations of time-frequency analysis
• Regular variation and differential equations
• Linear independence of time frequency translates for special configurations
• The noncommutative Wiener lemma, linear independence, and spectral properties of the algebra of time-frequency shift operators
• Growth Properties of Functions in Hardy Fields
• Von Neumann algebras and linear independence of translates
• Fine separation of average time complexity classes
• Linear independence of time-frequency translates
• Tauberian Theory
• Linear independence of time-frequency translates of functions with faster than exponential decay
• Integration in Finite Terms
• On the Linear Logarithmico-Exponential Differential Equation of the Second Order
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