Affine Density in Wavelet Analysis

✍ Scribed by Gitta Kutyniok (auth.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 2007
• Tongue: English
• Leaves: 149
• Series: Lecture Notes in Mathematics 1914
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages I-XII
Introduction....Pages 1-10
Wavelet and Gabor Frames....Pages 11-20
Weighted Affine Density....Pages 21-33
Qualitative Density Conditions....Pages 35-57
Quantitative Density Conditions....Pages 59-86
Homogeneous Approximation Property....Pages 87-104
Weighted Beurling Density and Shift-Invariant Gabor Systems....Pages 105-125
Back Matter....Pages 127-142

✦ Subjects

Fourier Analysis; Information and Communication, Circuits