Affine Density in Wavelet Analysis

  • Gitta¬†Kutyniok

Part of the Lecture Notes in Mathematics book series (LNM, volume 1914)

Table of contents

About this book

Introduction

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.

Keywords

affine density algorithms applied harmonic analysis calculus frames wavelets

Authors and affiliations

  • Gitta¬†Kutyniok
    • 1
    • 2
  1. 1.Program in Applied and Computational MathematicsPrinceton UniversityPrincetonUSA
  2. 2.Department of StatisticsStanford UniversityStanfordUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-540-72949-5
  • Copyright Information Springer-Verlag Berlin Heidelberg 2007
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-540-72916-7
  • Online ISBN 978-3-540-72949-5
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book