Affine Density in Wavelet Analysis (Lecture Notes in Mathematics #1914)
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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.
Details
- Publisher
- Springer Berlin Heidelberg
- Author
- Gitta Kutyniok
- Format
- Paperback
- Published
- Jul 12, 2007
- ISBN-13
- 9783540729167
- Pages
- 143
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