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Affine Density in Wavelet Analysis
Paperback
Series: Lecture Notes in Mathematics, Book 1914
ISBN13: 9783540729167
Publisher: Springer Nature
Published: Jul 12 2007
Pages: 143
Weight: 0.50
Height: 0.38 Width: 6.61 Depth: 9.21
Language: English
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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