Affine Density in Wavelet Analysis [electronic resource] / by Gitta Kutyniok.
Material type: TextSeries: Lecture Notes in Mathematics ; 1914Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2007Description: XII, 143 p. online resourceContent type:- text
- computer
- online resource
- 9783540729495
- 515.2433 23
- QA403.5-404.5
Wavelet and Gabor Frames -- Weighted Affine Density -- Qualitative Density Conditions -- Quantitative Density Conditions -- Homogeneous Approximation Property -- Weighted Beurling Density and Shift-Invariant Gabor Systems.
In wavelet analysis, irregular wavelet frames have recently come to the forefront of current research due to questions concerning the robustness and stability of wavelet algorithms. A major difficulty in the study of these systems is the highly sensitive interplay between geometric properties of a sequence of time-scale indices and frame properties of the associated wavelet systems. This volume provides the first thorough and comprehensive treatment of irregular wavelet frames by introducing and employing a new notion of affine density as a highly effective tool for examining the geometry of sequences of time-scale indices. Many of the results are new and published for the first time. Topics include: qualitative and quantitative density conditions for existence of irregular wavelet frames, non-existence of irregular co-affine frames, the Nyquist phenomenon for wavelet systems, and approximation properties of irregular wavelet frames.
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