Fredholm and Local Spectral Theory, with Applications to Multipliers

Book Description

This book shows the deep interaction between two important theories: Fredholm and local spectral theory. A particular emphasis is placed on the applications to multipliers and in particular to convolution operators. The book also presents some important progress, made in recent years, in the study of perturbation theory for classes of operators which occur in Fredholm theory.

Wavelets through a Looking Glass (Applied and Numerical Harmonic Analysis)

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A masterpiece in wavelets
Distinguished link between math and computer science
A fresh look at wavelets
an intriguing new wavelet book
An Intriguiging New Book

Wavelets through a Looking Glass (Applied and Numerical Harmonic Analysis)
Ola Bratteli , and Palle Jorgensen
Manufacturer: Birkhäuser Boston
ProductGroup: Book
Binding: Hardcover

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Analysis and Probability: Wavelets, Signals, Fractals (Graduate Texts in Mathematics)
A Wavelet Tour of Signal Processing, Second Edition (Wavelet Analysis & Its Applications)
The Malliavin Calculus (Dover Books on Mathematics)

ASIN: 0817642803

Book Description

This book combining wavelets and the world of the spectrum focuses on recent developments in wavelet theory, emphasizing fundamental and relatively timeless techniques that have a geometric and spectral-theoretic flavor. The exposition is clearly motivated and unfolds systematically, aided by numerous graphics. This self-contained book deals with important applications to signal processing, communications engineering, computer graphics algorithms, qubit algorithms and chaos theory, and is aimed at a broad readership of graduate students, practitioners, and researchers in applied mathematics and engineering. The book is also useful for other mathematicians with an interest in the interface between mathematics and communication theory.

Customer Reviews:

A masterpiece in wavelets.......2003-03-14

This is a very well written book on the theory of wavelets and its applications. The presentation is self-contained and may serve as an introduction for someone who wants to learn about this topic. It also is an excellent book for those who have an advanced graduate degree in applied mathematics since it demonstrates how to truly understand complex concepts. This book gives a general presentation of some recent developments in wavelet theory with an emphasis on techniques that have a geometric and spectral-theoretic flavor. It can be certainly used as a textbook for graduate students as well as as a reference book for the specialists and researchers. A very nice feature of the book are the tutorials at the beginning of each chapter and some sections, which serve as summaries of main ideas and guides through the background ideas and motivation. At the end of every chapter there are plenty of excercises of various level of difficulty. Overall, this is a great book and I recommend it highly to a motivated reader.

Distinguished link between math and computer science.......2003-03-11

This is an important mathematical reference written in excellent style. Wavelets have found applications in many areas of engineering and CS. The authors provide a detailed, rich and entertaining tour through this relatively young but important field for both math and CS/Eng. Connections are, e.g., made between advanced CS virtual-reality applications such as audio-systems processing, future applications such as quantum computing, and advanced math in functional analysis and operator theory.

A fresh look at wavelets.......2002-10-08

The Book by Bratteli and Jorgensen is a superb book on wavelet's theory. It is very well written and has new and a fresh point of view on the subject. Although there are several good books on wavelets, the book by Bratteli and Jorgensen covers an important niche that has not been covered before. In particular

1- The book covers the theory of wavelets from the point of view of operators and functional analysis and will appeal to a growing number of pure as well as applied mathematicians interested in the subject.

2- The writing of the book is very appealing: every chapter starts by a tutorial that gives motivation as well as intuition. It is then followed by a very clean mathematical development of the subject, together with many examples, figures, and applications from physics and engineering. A set of nice problems is provided at the end of each chapter. Thus this book can be used as a graduate textbook or for mathematical seminars in mathematics departments.

3- This book can even be used by experts in wavelet theory for learning about recent developments and new perspectives from operator theory and functional analysis.

I highly recommend this book.

an intriguing new wavelet book.......2002-09-09

This is a book about an important topic in applied mathematics by two authors with excellent credentials in both pure and applied areas. The reader will find many intriguing threads connecting wavelets to other parts of mathematics, including a wavelet index theorem, quantum computing, the ubiquitous C*-algebras O_n and, of course, spectral theory. The graphics are meticulously done.

I look forward to learning a lot from it.

An Intriguiging New Book.......2002-08-30

This is a book about an important topic in applied mathematics by two authors with excellent
credentials in both pure and applied areas.

Book Description

During the past two decades, pseudospectral methods have emerged as successful, and often superior, alternatives to better known computational procedures, such as finite difference and finite element methods of numerical solution, in several key application areas. These areas include computational fluid dynamics, wave motion, and weather forecasting. This book explains how, when and why this pseudospectral approach works. In order to make the subject accessible to students as well as researchers and engineers, the author presents the subject using illustrations, examples, heuristic explanations, and algorithms rather than rigorous theoretical arguments. This book will be of interest to graduate students, scientists, and engineers interested in applying pseudospectral methods to real problems.

Customer Reviews:

This is a guide, not an expository report.......2003-03-01

This book is a wonderful guide to pseudo-spectral techniques which begins its discussion as an extension or more precisely as the limit of finite difference techniques. Unfortunately for anyone who would wish to learn these techniques I would have to recomend another book. However, for someone who already knows these techniques then this book is invaluable. It covers in a clear, mathematical way in which certain pitfalls and problems may be overcome. It does not, however, teach more of the advanced methods that must be used in more complex boundary value problems.

Book Description

This book gives a comprehensive picture of the present stage of development of spectral analysis and filter theory in geophysics. The principles and theories behind classical and modern methods are described and the effectiveness of these methods is assessed; selected examples of their practical application in geophysics are discussed. The modern methods include, for example, spectral analysis by fitting random models to the data, the maximum-entropy and maximum-likelihood spectral analysis procedures, the Wiener and Kalman filters, homomorphic deconvolution, and adaptive procedures for non-stationary processes. This book represents a valuable aid in education and research and for solving practical problems in geophysics and related disciplines.

Pseudodifferential Operators and Spectral Theory (Springer Series in Soviet Mathematics)

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Pseudodifferential Operators and Spectral Theory (Springer Series in Soviet Mathematics)
M.A. Shubin
Manufacturer: Springer
ProductGroup: Book
Binding: Paperback

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ASIN: 354041195X

Book Description

This is the second edition of Shubin's classical book. It provides an introduction to the theory of pseudodifferential operators and Fourier integral operators from the very basics. The applications discussed include complex powers of elliptic operators, Hörmander asymptotics of the spectral function and eigenvalues, and methods of approximate spectral projection. Exercises and problems are included to help the reader master the essential techniques. The book is written for a wide audience of mathematicians, be they interested students or researchers.

Spectral Analysis for Physical Applications

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Excellent exposition of modern power spectrum ananysis

Spectral Analysis for Physical Applications
Donald B. Percival , and Andrew T. Walden
Manufacturer: Cambridge University Press
ProductGroup: Book
Binding: Paperback

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Wavelet Methods for Time Series Analysis (Cambridge Series in Statistical and Probabilistic Mathematics)
Spectral Analysis of Time-Series Data
Time Series: Data Analysis and Theory (Classics in Applied Mathematics, 36) (Classics in Applied Mathematics)
Fourier Analysis of Time Series: An Introduction (Wiley Series in Probability and Statistics)
Ripples in Mathematics

ASIN: 0521435412

Book Description

This book is an up-to-date introduction to univariate spectral analysis aimed at graduate students, which reflects a new scientific awareness of spectral complexity, as well as the widespread use of spectral analysis on digital computers with considerable computational power. The text provides theoretical and computational guidance on the available techniques, emphasizing those that work in practice. It gives equal weight to both algorithms and statistical theory and is valuable for the many examples it gives showing the application of spectral analysis to real data sets. The book is unique in placing special emphasis on the multitaper technique, which can successfully handle spectra with intricate structure and data with or without spectral lines. The text contains a large number of exercises.

Customer Reviews:

Excellent exposition of modern power spectrum ananysis.......2000-09-01

A splendid overview of modern power spectrum analysis, with an emphasis on multitaper methods. Perfect for any scientist or engineer who deals with time series data.

Maximum Entropy and Bayesian Methods in Inverse Problems (Fundamental Theories of Physics)

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Maximum Entropy and Bayesian Methods in Inverse Problems (Fundamental Theories of Physics)

Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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ASIN: 9027720746

Spectral Theory and Differential Operators (Cambridge Studies in Advanced Mathematics)

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Spectral Theory and Differential Operators (Cambridge Studies in Advanced Mathematics)
E. Brian Davies
Manufacturer: Cambridge University Press
ProductGroup: Book
Binding: Paperback

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Heat Kernels and Spectral Theory (Cambridge Tracts in Mathematics)
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ASIN: 0521587107

Book Description

In this book, Davies introduces the reader to the theory of partial differential operators, up to the spectral theorem for bounded linear operators on Banach spaces. He also describes the theory of Fourier transforms and distributions as far as is needed to analyze the spectrum of any constant coefficient partial differential operator. He also presents a completely new proof of the spectral theorem for unbounded self-adjoint operators and demonstrates its application to a variety of second order elliptic differential operators. Finally, the book contains a detailed account of the application of variational methods to estimate the eigenvalues of operators with measurable coefficients defined by the use of quadratic form techniques. Illustrated with many examples, it is well-suited to graduate-level work.

Spectral Methods for Incompressible Viscous Flow

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Spectral Methods for Incompressible Viscous Flow
Roger Peyret
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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ASIN: 0387952217

Book Description

This well-written book explains the theory of spectral methods and their application to the computation of viscous incompressible fluid flows in clear and elementary terms. It begins with an introduction to the fundamentals of spectral methods and then moves on to cover, in particular, the Fourier and Chebyshev methods. Examples are included. Chapters 6 and 7 handle streamfunction-vorticity and velocity-pressure fomulations of the Navier-Stokes equations. Chapter 8 and 9 address special topics such as self- adaptive coordinate transform, treatment of singularities, and domain decomposition. The work will be useful to those teaching in the field at the graduate level, as well as to researchers working in the area.

Spectral Theory of the Riemann Zeta-Function (Cambridge Tracts in Mathematics)

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Spectral Theory of the Riemann Zeta-Function (Cambridge Tracts in Mathematics)
Y. Motohashi
Manufacturer: Cambridge University Press
ProductGroup: Book
Binding: Hardcover

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ASIN: 0521445205

Book Description

This ground-breaking work combines the classic (the zeta-function) with the modern (the spectral theory) to create a comprehensive but elementary treatment of spectral resolution. The story starts with a basic but unabridged treatment of the spectral resolution of the non-Euclidean Laplacian and the trace formulas. The author achieves this by the use of standard tools from analysis rather than any heavy machinery, forging a substantial aid for beginners in spectral theory. These ideas are then utilized to unveil a new image of the zeta-function, revealing it as the main gem of a necklace composed of all automorphic L-functions. In this book readers will find a detailed account of one of the most fascinating stories in the recent development of number theory. Mathematics specialists and researchers will find this a fascinating work.

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