Analysis and probability : wavelets, signals, fractals /

Analysis and probability : wavelets, signals, fractals /

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Bibliographic Details
Author / Creator:Jørgensen, Palle E. T., 1947-
Imprint:New York, NY : Springer, c2006.
Description:xliv, 276 p. : ill. ; 24 cm.
Language:English
Series:Graduate texts in mathematics ; 234
Subject:
Mathematical analysis.
Probabilities.
Wavelets (Mathematics)
Fractals.
Fractals.
Mathematical analysis.
Probabilities.
Wavelets (Mathematics)
Format: Print Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/6162315
Hidden Bibliographic Details
Other authors / contributors:Treadway, Brian.
ISBN:0387295194
9780387295190
0387330828 (e-isbn)
9780387330822 (e-isbn)
Notes:Includes bibliographical references.
Standard no.:9780387295190
Table of Contents:
  • Preface
  • Getting started
  • An apology
  • Glossary
  • Multiresolutions
  • Prerequisites and cross-audience
  • Aim and scope
  • Self-similarity
  • New issues, new tools
  • List of names and discoveries
  • General theory
  • A word about the graphics and the illustrations
  • Special features of the book
  • Exercises: Overview
  • Figures. Read Me!
  • Acknowledgments
  • 1. Introduction: Measures on path space
  • Prerequisites
  • Prelude
  • 1.1. Wavelets
  • 1.2. Path space
  • 1.3. Multiresolutions
  • 1.4. Sampling
  • 1.5. A convergence theorem for infinite products
  • 1.6. A brief outline
  • 1.7. From wavelets to fractals
  • Exercises
  • History
  • References and remarks
  • 2. Transition probabilities: Random walk
  • Prerequisites
  • Prelude
  • 2.1. Standing assumptions
  • 2.2. An example
  • 2.3. Some definitions: The Ruelle operator, harmonic functions, cocycles
  • 2.4. Existence of the measures P[subscript x]
  • 2.5. Kolmogorov's consistency condition
  • 2.6. The probability space [Omega]
  • 2.7. A boundary representation for harmonic functions
  • 2.8. Invariant measures
  • Exercises
  • References and remarks
  • 3. N[subscript 0] vs. Z
  • Prerequisites
  • Prelude
  • 3.1. Terminology
  • 3.2. The unit interval
  • 3.3. A sufficient condition for P[subscript x] (Z) = 1
  • Exercises
  • References and remarks
  • 4. A case study: Duality for Cantor sets
  • Prerequisites
  • Prelude
  • 4.1. Affine iterated function systems: The general case
  • 4.2. The quarter Cantor set: The example W(x) = cos[superscript 2] (2[Pi]x)
  • 4.3. The conjugate Cantor set, and a special harmonic function
  • 4.4. A sufficient condition for P[subscript x] (N[subscript 0]) = 1
  • Conclusions
  • Exercises
  • References and remarks
  • 5. Infinite products
  • Prerequisites
  • Prelude
  • 5.1. Riesz products
  • 5.2. Random products
  • 5.3. The general case
  • 5.4. A uniqueness theorem
  • 5.5. Wavelets revisited
  • Exercises
  • References and remarks
  • 6. The minimal eigenfunction
  • Prerequisites
  • Prelude
  • 6.1. A general construction of h[subscript min]
  • 6.2. A closed expression for h[subscript min]
  • Exercises
  • References and remarks
  • 7. Generalizations and applications
  • Prerequisites
  • Prelude
  • 7.1. Translations and the spectral theorem
  • 7.2. Multiwavelets and generalized multiresolution analysis (GMRA)
  • 7.3. Operator-coefficients
  • 7.4. Operator-valued measures
  • 7.5. Wavelet packets
  • 7.6. Representations of the Cuntz algebra O[subscript 2]
  • 7.7. Representations of the algebra of the canonical anticommutation relations (CARs)
  • Exercises
  • References and remarks
  • 8. Pyramids and operators
  • Prerequisites
  • Prelude
  • 8.1. Why pyramids
  • 8.2. Dyadic wavelet packets
  • 8.3. Measures and decompositions
  • 8.4. Multiresolutions and tensor products
  • Exercises
  • References and remarks
  • 9. Pairs of representations of the Cuntz algebras O[subscript n], and their application to multiresolutions
  • Prerequisites
  • Prelude
  • 9.1. Factorization of unitary operators in Hilbert space
  • 9.2. Generalized multiresolutions
  • 9.3. Permutation of bases in Hilbert space
  • 9.4. Tilings
  • 9.5. Applications to wavelets
  • 9.6. An application to fractals
  • 9.7. Phase modulation
  • Exercises
  • References and remarks
  • Appendices: Polyphase matrices and the operator algebra O[subscript N]
  • Prerequisites
  • Prelude
  • Appendix A. Signals and filters
  • Appendix B. Hilbert space and systems of operators
  • Appendix C. A tale of two Hilbert spaces
  • Table C.1. Operations on two Hilbert spaces: The correspondence principle
  • Appendix D. Signal processing, matrices, and programming diagrams
  • References and remarks: Systems theory
  • Afterword
  • Comments on signal/image processing terminology
  • Introduction
  • JPEG 2000 vs. GIF
  • JPEG 2000
  • GIF
  • Grayscale
  • Quadrature-mirror filter
  • What is a frame?
  • To the mathematics student
  • To an engineer
  • Alias (aliasing)
  • Engineering
  • Mathematics
  • Computational mathematics
  • Epigraphs
  • References
  • Symbols
  • Index

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