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Titlebook: Advances in Gabor Analysis; Hans G. Feichtinger,Thomas Strohmer Book 2003 Springer Science+Business Media New York 2003 Potential.Signal.a

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期刊全称Advances in Gabor Analysis
影响因子2023Hans G. Feichtinger,Thomas Strohmer
视频video
学科分类Applied and Numerical Harmonic Analysis
图书封面Titlebook: Advances in Gabor Analysis;  Hans G. Feichtinger,Thomas Strohmer Book 2003 Springer Science+Business Media New York 2003 Potential.Signal.a
影响因子The Applied and Numerical Harmonic Analysis (ANHA) book series aims to provide the engineering, mathematical, and scientific communities with significant developments in harmonic analysis, ranging from abstract har­ monic analysis to basic applications. The title of the series reflects the im­ portance of applications and numerical implementation, but richness and relevance of applications and implementation depend fundamentally on the structure and depth of theoretical underpinnings. Thus, from our point of view, the interleaving of theory and applications and their creative symbi­ otic evolution is axiomatic. Harmonic analysis is a wellspring of ideas and applicability that has flour­ ished, developed, and deepened over time within many disciplines and by means of creative cross-fertilization with diverse areas. The intricate and fundamental relationship between harmonic analysis and fields such as sig­ nal processing, partial differential equations (PDEs), and image processing is reflected in our state of the art ANHA series. Our vision of modern harmonic analysis includes mathematical areas such as wavelet theory, Banach algebras, classical Fourier analysis, time­ frequency ana
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Chemosensors of Ion and Molecule Recognitionrestricted to a suitable interval. Dual bases and Riesz bounds are given explicitly. The construction is based on a Zak transform for periodic functions and an unfolding operator for periodic Wilson bases. Fast algorithms for analysis and synthesis are described.
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https://doi.org/10.1007/978-94-011-3973-1 are studied in continuous and discrete time setting. Explicit solutions are found in Zak transform domain. The optimizers turn out to be generically ill-localized similar to the no-go Balian—Low theorem.
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https://doi.org/10.1385/1592598897ique Gabor duals (within the subspaces). Finally, we provide a necessary and sufficient condition for a square-integrable function g to generate a subspace Gabor frame in the one-dimensional, rational case. The condition is phrased in terms of the Zak transform of ..
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