Wavelets And Renormalization

Author : Guy Battle
Publisher : World Scientific
Page : 582 pages
File Size : 47,7 Mb
Release : 1999
Category : Science
ISBN : 9810226241

Get Book

Wavelets and Renormalization by Guy Battle Pdf

WAVELETS AND RENORMALIZATION describes the role played by wavelets in Euclidean field theory and classical statistical mechanics. The author begins with a stream-lined introduction to quantum field theory from a rather basic point of view. Functional integrals for imaginary-time-ordered expectations are introduced early and naturally, while the connection with the statistical mechanics of classical spin systems is introduced in a later chapter.A vastly simplified (wavelet) version of the celebrated Glimm-Jaffe construction of the 3 quantum field theory is presented. It is due to Battle and Federbush, and it bases an inductively defined cluster expansion on a wavelet decomposition of the Euclidean quantum field. The presentation is reserved for the last chapter, while the more basic aspects of cluster expansions are reviewed in the chapter on classical spin systems.Wavelets themselves are studied from two different points of view arising from two disciplines. The mathematical point of view covers the basic properties of wavelets and methods for constructing well-known wavelets such as Meyer wavelets, Daubechies wavelets, etc. The physical point of view covers the renormalization group formalism, where there is a close connection between wavelets and Gaussian fixed points.The book is heavily mathematical, but avoids the theorem-proof-theorem-proof format in the interests of preserving the flow of the discussion i.e., it is written in the style of an old-fashioned theoretical physics book, but the major claims are rigorously proven. The minor themes of the book are reflection positivity, the combinatorics of cluster expansions, and the issue of phase transitions themes which have nothing to do with wavelets, but which provide necessary cultural background for the physical context."

Author : Guy Battle
Publisher : World Scientific
Page : 588 pages
File Size : 41,5 Mb
Release : 1999-03-03
Category : Mathematics
ISBN : 9789814499125

Get Book

Wavelets And Renormalization by Guy Battle Pdf

WAVELETS AND RENORMALIZATION describes the role played by wavelets in Euclidean field theory and classical statistical mechanics. The author begins with a stream-lined introduction to quantum field theory from a rather basic point of view. Functional integrals for imaginary-time-ordered expectations are introduced early and naturally, while the connection with the statistical mechanics of classical spin systems is introduced in a later chapter.A vastly simplified (wavelet) version of the celebrated Glimm-Jaffe construction of the Φ43 quantum field theory is presented. It is due to Battle and Federbush, and it bases an inductively defined cluster expansion on a wavelet decomposition of the Euclidean quantum field. The presentation is reserved for the last chapter, while the more basic aspects of cluster expansions are reviewed in the chapter on classical spin systems.Wavelets themselves are studied from two different points of view arising from two disciplines. The mathematical point of view covers the basic properties of wavelets and methods for constructing well-known wavelets such as Meyer wavelets, Daubechies wavelets, etc. The physical point of view covers the renormalization group formalism, where there is a close connection between wavelets and Gaussian fixed points.The book is heavily mathematical, but avoids the theorem-proof-theorem-proof format in the interests of preserving the flow of the discussion — i.e., it is written in the style of an old-fashioned theoretical physics book, but the major claims are rigorously proven. The minor themes of the book are reflection positivity, the combinatorics of cluster expansions, and the issue of phase transitions — themes which have nothing to do with wavelets, but which provide necessary cultural background for the physical context.

Author : Lokenath Debnath
Publisher : Springer Science & Business Media
Page : 450 pages
File Size : 47,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461200253

Get Book

Wavelets and Signal Processing by Lokenath Debnath Pdf

Provides a digest of the current developments, open questions and unsolved problems likely to determine a new frontier for future advanced study and research in the rapidly growing areas of wavelets, wavelet transforms, signal analysis, and signal and image processing. Ideal reference work for advanced students and practitioners in wavelets, and wavelet transforms, signal processing and time-frequency signal analysis. Professionals working in electrical and computer engineering, applied mathematics, computer science, biomedical engineering, physics, optics, and fluid mechanics will also find the book a valuable resource.

Author : M.V. Altaisky
Publisher : Universities Press
Page : 168 pages
File Size : 54,6 Mb
Release : 2005-02
Category : Wavelets (Mathematics)
ISBN : 8173715033

Get Book

Wavelets:Theory,Applications,Implementation by M.V. Altaisky Pdf

Author : Lokenath Debnath
Publisher : Springer Science & Business Media
Page : 444 pages
File Size : 51,7 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9781461201373

Get Book

Wavelet Transforms and Time-Frequency Signal Analysis by Lokenath Debnath Pdf

The last fifteen years have produced major advances in the mathematical theory of wavelet transforms and their applications to science and engineering. In an effort to inform researchers in mathematics, physics, statistics, computer science, and engineering and to stimulate furtherresearch, an NSF-CBMS Research Conference on Wavelet Analysis was organized at the University of Central Florida in May 1998. Many distinguished mathematicians and scientists from allover the world participated in the conference and provided a digest of recent developments, open questions, and unsolved problems in this rapidly growing and important field. As a follow-up project, this monograph was developed from manuscripts sub mitted by renowned mathematicians and scientists who have made important contributions to the subject of wavelets, wavelet transforms, and time-frequency signal analysis. This publication brings together current developments in the theory and applications of wavelet transforms and in the field of time-frequency signal analysis that are likely to determine fruitful directions for future advanced study and research.

Author : Serge Dubuc,Gilles Deslauriers
Publisher : American Mathematical Soc.
Page : 412 pages
File Size : 40,8 Mb
Release : 1999-01-01
Category : Mathematics
ISBN : 0821870181

Get Book

Spline Functions and the Theory of Wavelets by Serge Dubuc,Gilles Deslauriers Pdf

This work is based on a series of thematic workshops on the theory of wavelets and the theory of splines. Important applications are included. The volume is divided into four parts: Spline Functions, Theory of Wavelets, Wavelets in Physics, and Splines and Wavelets in Statistics. Part one presents the broad spectrum of current research in the theory and applications of spline functions. Theory ranges from classical univariate spline approximation to an abstract framework for multivariate spline interpolation. Applications include scattered-data interpolation, differential equations and various techniques in CAGD. Part two considers two developments in subdivision schemes; one for uniform regularity and the other for irregular situations. The latter includes construction of multidimensional wavelet bases and determination of bases with a given time frequency localization. In part three, the multifractal formalism is extended to fractal functions involving oscillating singularites. There is a review of a method of quantization of classical systems based on the theory of coherent states. Wavelets are applied in the domains of atomic, molecular and condensed-matter physics. In part four, ways in which wavelets can be used to solve important function estimation problems in statistics are shown. Different wavelet estimators are proposed in the following distinct cases: functions with discontinuities, errors that are no longer Gaussian, wavelet estimation with robustness, and error distribution that is no longer stationary. Some of the contributions in this volume are current research results not previously available in monograph form. The volume features many applications and interesting new theoretical developments. Readers will find powerful methods for studying irregularities in mathematics, physics, and statistics.

Author : Gerard Meurant
Publisher : Academic Press
Page : 723 pages
File Size : 40,7 Mb
Release : 2012-12-02
Category : Technology & Engineering
ISBN : 9780323139748

Get Book

Wavelets by Gerard Meurant Pdf

Wavelets: A Tutorial in Theory and Applications is the second volume in the new series WAVELET ANALYSIS AND ITS APPLICATIONS. As a companion to the first volume in this series, this volume covers several of the most important areas in wavelets, ranging from the development of the basic theory such as construction and analysis of wavelet bases to an introduction of some of the key applications, including Mallat's local wavelet maxima technique in second generation image coding. A fairly extensive bibliography is also included in this volume. Covers several of the most important areas in wavelets, ranging from the development of the basic theory, such as: Construction and analysis of wavelet bases Introduction of some of the key applications, including Mallat's local wavelet maxima technique in second generation image coding Extensive bibliography is also included in this volume Companion to the first volume in this series, An Introduction to Wavelets, and can be used as supplementary instructional material for a two-semester course on wavelet analysis

Author : Lokenath Debnath
Publisher : Springer Science & Business Media
Page : 575 pages
File Size : 41,9 Mb
Release : 2011-06-28
Category : Technology & Engineering
ISBN : 9781461200970

Get Book

Wavelet Transforms and Their Applications by Lokenath Debnath Pdf

Overview Historically, the concept of "ondelettes" or "wavelets" originated from the study of time-frequency signal analysis, wave propagation, and sampling theory. One of the main reasons for the discovery of wavelets and wavelet transforms is that the Fourier transform analysis does not contain the local information of signals. So the Fourier transform cannot be used for analyzing signals in a joint time and frequency domain. In 1982, Jean MorIet, in collaboration with a group of French engineers, first introduced the idea of wavelets as a family of functions constructed by using translation and dilation of a single function, called the mother wavelet, for the analysis of nonstationary signals. However, this new concept can be viewed as the synthesis of various ideas originating from different disciplines including mathematics (Calder6n-Zygmund operators and Littlewood-Paley theory), physics (coherent states in quantum mechanics and the renormalization group), and engineering (quadratic mirror filters, sideband coding in signal processing, and pyramidal algorithms in image processing). Wavelet analysis is an exciting new method for solving difficult problems in mathematics, physics, and engineering, with modern applications as diverse as wave propagation, data compression, image processing, pattern recognition, computer graphics, the detection of aircraft and submarines, and improvement in CAT scans and other medical image technology. Wavelets allow complex information such as music, speech, images, and patterns to be decomposed into elementary forms, called the fundamental building blocks, at different positions and scales and subsequently reconstructed with high precision.

Author : Jean-Pierre Antoine,Romain Murenzi,Pierre Vandergheynst,Syed Twareque Ali
Publisher : Cambridge University Press
Page : 478 pages
File Size : 48,6 Mb
Release : 2008-06-12
Category : Technology & Engineering
ISBN : 9781139453141

Get Book

Two-Dimensional Wavelets and their Relatives by Jean-Pierre Antoine,Romain Murenzi,Pierre Vandergheynst,Syed Twareque Ali Pdf

Two-dimensional wavelets offer a number of advantages over discrete wavelet transforms, in particular for analysis of real-time signals. This book provides thorough and comprehensive treatment of 2-D wavelets, with extensive use of practical applications and illustrative examples throughout. For engineers, physicists and mathematicians.

Author : Ingrid Daubechies
Publisher : SIAM
Page : 357 pages
File Size : 54,7 Mb
Release : 1992-01-01
Category : Science
ISBN : 1611970105

Get Book

Ten Lectures on Wavelets by Ingrid Daubechies Pdf

Wavelets are a mathematical development that may revolutionize the world of information storage and retrieval according to many experts. They are a fairly simple mathematical tool now being applied to the compression of data--such as fingerprints, weather satellite photographs, and medical x-rays--that were previously thought to be impossible to condense without losing crucial details. This monograph contains 10 lectures presented by Dr. Daubechies as the principal speaker at the 1990 CBMS-NSF Conference on Wavelets and Applications. The author has worked on several aspects of the wavelet transform and has developed a collection of wavelets that are remarkably efficient.

Author : Yves Meyer,Sylvie Roques
Publisher : Atlantica Séguier Frontières
Page : 808 pages
File Size : 44,5 Mb
Release : 1993
Category : Wavelets
ISBN : 2863321307

Get Book

Progress in Wavelet Analysis and Applications by Yves Meyer,Sylvie Roques Pdf

Author : Daniel Alpay
Publisher : Springer Science & Business Media
Page : 197 pages
File Size : 53,7 Mb
Release : 2006-08-06
Category : Mathematics
ISBN : 9783764375881

Get Book

Wavelets, Multiscale Systems and Hypercomplex Analysis by Daniel Alpay Pdf

This volume contains a selection of papers on the topics of Clifford analysis and wavelets and multiscale analysis, the latter being understood in a very wide sense. The theory of wavelets is mathematically rich and has many practical applications. Most of the articles have been written on invitation and they provide a unique collection of material, particularly relating to Clifford analysis and the theory of wavelets.

Author : Gordon Erlebacher,M. Yousuff Hussaini,Leland M. Jameson
Publisher : Oxford University Press on Demand
Page : 523 pages
File Size : 46,9 Mb
Release : 1996
Category : History
ISBN : 9780195094237

Get Book

Wavelets by Gordon Erlebacher,M. Yousuff Hussaini,Leland M. Jameson Pdf

Wavelets are spatially localized functions whose amplitude drops off exponentially outside a small "window". They are used to magnify experimental or numerical data and have become powerful tools in signal processing and other computational sciences. This book gives scientists and engineers a practical understanding of wavelets--their origins, their purpose, their use, and their prospects. It covers the applications of wavelets as a diagnostic tool and the use of wavelet basis functions to solve differential equations. Each chapter was written by one of five lecturers of a course sponsored by the Institute of Computer Applications in Science and Engineering (ICASE) and the NASA Langley Research Center. Not only does this book treat the latest advances on the subject, but it also attempts to impart practical knowledge to allow scientists and engineers to evaluate objectively where these tools stand in relation to their needs.

Author : Mary Beth Ruskai
Publisher : Jones & Bartlett Publishers
Page : 500 pages
File Size : 42,7 Mb
Release : 1992
Category : Mathematics
ISBN : UOM:39015049377578

Get Book

Wavelets and Their Applications by Mary Beth Ruskai Pdf

Contributions discuss signal analysis discrete-time signal processing, wavelets for Quincunx pyramid, transform maxima and multiscale edges, among other topics; numerical analysis; other applications the optical wave transform, continuous wavelet transform, quantum mechanics; and theoretical develop

Author : John J. Benedetto
Publisher : CRC Press
Page : 592 pages
File Size : 43,8 Mb
Release : 2021-07-28
Category : Mathematics
ISBN : 9781000443462

Get Book

Wavelets by John J. Benedetto Pdf

Wavelets is a carefully organized and edited collection of extended survey papers addressing key topics in the mathematical foundations and applications of wavelet theory. The first part of the book is devoted to the fundamentals of wavelet analysis. The construction of wavelet bases and the fast computation of the wavelet transform in both continuous and discrete settings is covered. The theory of frames, dilation equations, and local Fourier bases are also presented. The second part of the book discusses applications in signal analysis, while the third part covers operator analysis and partial differential equations. Each chapter in these sections provides an up-to-date introduction to such topics as sampling theory, probability and statistics, compression, numerical analysis, turbulence, operator theory, and harmonic analysis. The book is ideal for a general scientific and engineering audience, yet it is mathematically precise. It will be an especially useful reference for harmonic analysts, partial differential equation researchers, signal processing engineers, numerical analysts, fluids researchers, and applied mathematicians.