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"Wavelets (Mathematics)"
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Differential Equations
Differential Equations: A Modern Approach with Wavelets is the newest book from one of the most published authors in all of mathematics is an attempt to offer a new, more modern take on the Differential Equations course. The world is changing. Because of the theory of wavelets, Fourier analysis is ever more important and central. Plus, applications are a driving force behind much of mathematics.
This text presents a more balanced picture. It covers differential equations (both ordinary and partial), Fourier analysis, and applications in equal measure and with equal weight. The Riemann integral is used throughout. The author does not assume that the student knows any functional analysis. Likewise, he does not assume that the student has had a course in undergraduate real analysis. To make the book timely and exciting, a substantial chapter on basic properties of wavelets, with applications to signal processing and image processing, is included. This should give students and instructors alike a taste of what is happening in the subject today.
Features
Provides a new approach to the Differential Equations course from one of the most widely published authors in mathematics
There is not a textbook quite like this one; a similar approach is taken for the separate Partial Differential Equations course, but this is new to the subject
The book can be used for several courses in the advanced mathematics curriculum, while aimed at more prepared students
Features numerous problems and exercises throughout the text
eBook
A wavelet tour of signal processing : the sparse way
Mallat's book is the undisputed reference in this field - it is the only one that covers the essential material in such breadth and depth.- Laurent Demanet, Stanford UniversityThe new edition of this classic book gives all the major concepts, techniques and applications of sparse representation, reflecting the key role the subject plays in.
eBook
Wave Front Set of Solutions to Sums of Squares of Vector Fields
We study the (micro)hypoanalyticity and the Gevrey hypoellipticity of sums of squares of vector fields in terms of the Poisson–Treves
stratification. The FBI transform is used. We prove hypoanalyticity for several classes of sums of squares and show that our method,
though not general, includes almost every known hypoanalyticity result. Examples are discussed.
eBook
An introduction to wavelet theory in finance
This book offers an introduction to wavelet theory and provides the essence of wavelet analysis — including Fourier analysis and spectral analysis; the maximum overlap discrete wavelet transform; wavelet variance, covariance, and correlation — in a unified and friendly manner. It aims to bridge the gap between theory and practice by presenting substantial applications of wavelets in economics and finance.
eBook
One-Dimensional Dyadic Wavelets
The theory of wavelets has been thoroughly studied by many authors; standard references include books by I. Daubechies, by Y. Meyer,
by R. Coifman and Y. Meyer, by C.K. Chui, and by M.V. Wickerhauser. In addition, the development of wavelets influenced the study of
various other reproducing function systems. Interestingly enough, some open questions remained unsolved or only partially solved for
more than twenty years even in the most basic case of dyadic orthonormal wavelets in a single dimension. These include issues related to
the MRA structure (for example, a complete understanding of filters), the structure of the space of negative dilates (in particular,
with respect to what is known as the Baggett problem), and the variety of resolution structures that may occur. In this article we offer
a comprehensive, yet technically fairly elementary approach to these questions. On this path, we present a multitude of new results,
resolve some of the old questions, and provide new advances for some problems that remain open for the future.
In this study, we
have been guided mostly by the philosophy presented some twenty years ago in a book by E. Hernandez and G. Weiss (one of us), in which
the orthonormal wavelets are characterized by four basic equations, so that the interplay between wavelets and Fourier analysis provides
a deeper insight into both fields of research. This book has influenced hundreds of researchers, and their effort has produced a variety
of new techniques, many of them reaching far beyond the study of one-dimensional orthonormal wavelets. Here we are trying to close the
circle in some sense by applying these new techniques to the original subject of one-dimensional wavelets. We are primarily interested
in the quality of new results and their clear presentations; for this reason, we keep our study on the level of a single dimension,
although we are aware that many of our results can be extended beyond that case.
Given
Given a principal shift invariant space
The third and final chapter is devoted to the second case, i.e., when the space
eBook
Mathematical analysis, wavelets, and signal processing : an International Conference on Mathematical Analysis and Signal Processing, January 3-9, 1994, Cairo University, Cairo, Egypt
This book contains the proceedings of an international conference held in Cairo, Egypt (January 1994). This glorious ancient city was the gathering place for mathematicians and engineers to exchange ideas and to discuss new research trends. Mathematics and engineering discoveries, such as wavelets, multiresolution analysis, and subband coding schemes, caused rapid advancements in signal processing, necessitating an interdisciplinary approach. Contributors to this conference demonstrated that some traditional areas of mathematical analysis - sampling theory, approximation theory, and orthogonal polynomials - have proven extremely useful in solving various signal processing problems.This book features P. L. Butzer on...\"\"Mathematics in Egypt and Its Connections with the Court School of Charlemagne\"\".With several articles discussing the most recent advances and new trends in mathematical analysis and signal processing, this book emphasizes interactions between mathematics and electrical engineering.
eBook
