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Mathematics - Analysis | Affine Density in Wavelet Analysis

Affine Density in Wavelet Analysis

Series: Lecture Notes in Mathematics, Vol. 1914

Kutyniok, Gitta

2007, XII, 143 p. With online files/update.

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  • About this book

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.

Content Level » Research

Keywords » affine density - algorithms - applied harmonic analysis - calculus - frames - wavelets

Related subjects » Analysis - Applications

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