Affine Density in Wavelet Analysis (Lecture Notes in Mathematics)
By Gitta Kutyniok
* Publisher: Springer
* Number Of Pages: 142
* Publication Date: 2007-08
* Sales Rank:
* ISBN / ASIN: 354072916X
* EAN: 9783540729167
* Binding: Paperback
* Manufacturer: Springer
* Studio: Springer
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Book Description:
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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