On accumulated spectrograms for Gabor frames

IF 1.2 3区 数学 Q1 MATHEMATICS
Simon Halvdansson
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引用次数: 0

Abstract

Analogs of classical results on accumulated spectrograms, the sum of spectrograms of eigenfunctions of localization operators, are established for Gabor multipliers. We show that the lattice 1 distance between the accumulated spectrogram and the indicator function of the Gabor multiplier mask is bounded by the number of lattice points near the boundary of the mask and that this bound is sharp in general. The methods developed for the proofs are also used to show that the Weyl-Heisenberg ensemble restricted to a lattice is hyperuniform when the Gabor frame is tight.
关于 Gabor 帧的累积频谱图
我们为 Gabor 乘法器建立了累积谱图(局部化算子特征函数的谱图总和)经典结果的类比。我们证明了累积谱图与 Gabor 乘法器掩模的指示函数之间的晶格 ℓ1 距离受掩模边界附近的晶格点数的约束,而且这个约束在一般情况下是尖锐的。为证明而开发的方法还用于证明当 Gabor 框架紧密时,限制在网格上的韦尔-海森堡集合是超均匀的。
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来源期刊
CiteScore
2.50
自引率
7.70%
发文量
790
审稿时长
6 months
期刊介绍: The Journal of Mathematical Analysis and Applications presents papers that treat mathematical analysis and its numerous applications. The journal emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions. Papers are sought which employ one or more of the following areas of classical analysis: • Analytic number theory • Functional analysis and operator theory • Real and harmonic analysis • Complex analysis • Numerical analysis • Applied mathematics • Partial differential equations • Dynamical systems • Control and Optimization • Probability • Mathematical biology • Combinatorics • Mathematical physics.
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