Kutyniok Affine Density in Wavelet Analysis

Erscheinungsjahr 2007
ISBN: 978-3-540-72949-5
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 1914, 143 Seiten, eBook

Reihe: Lecture Notes in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Kutyniok, Gitta

Inhaltsverzeichnis

Wavelet and Gabor Frames.- Weighted Affine Density.- Qualitative Density Conditions.- Quantitative Density Conditions.- Homogeneous Approximation Property.- Weighted Beurling Density and Shift-Invariant Gabor Systems.