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  • Book
  • © 2007

Affine Density in Wavelet Analysis

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

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  • ISBN: 978-3-540-72949-5
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Table of contents (7 chapters)

  1. Front Matter

    Pages I-XII
  2. Introduction

    Pages 1-10
  3. Back Matter

    Pages 127-142

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.

Keywords

  • affine density
  • algorithms
  • applied harmonic analysis
  • calculus
  • frames
  • wavelets
  • information and communication, circuits

Authors and Affiliations

  • Program in Applied and Computational Mathematics, Princeton University, Princeton, USA

    Gitta Kutyniok

  • Department of Statistics, Stanford University, Stanford, USA

    Gitta Kutyniok

Bibliographic Information

Buying options

eBook
USD 34.99
Price excludes VAT (USA)
  • ISBN: 978-3-540-72949-5
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD 49.95
Price excludes VAT (USA)