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Author : Stéphane Jaffard
Publisher :
ISBN 13 : 9781470401726
Total Pages : 110 pages
Book Rating : 4.4/5 (17 download)
Download or read book Wavelet Methods for Pointwise Regularity and Local Oscillations of Functions written by Stéphane Jaffard and published by . This book was released on 1996 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Stphane Jaffard
Publisher : American Mathematical Soc.
ISBN 13 : 9780821863107
Total Pages : 132 pages
Book Rating : 4.8/5 (631 download)
Download or read book Wavelet Methods for Pointwise Regularity and Local Oscillations of Functions written by Stphane Jaffard and published by American Mathematical Soc.. This book was released on 1996-10-29 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: Currently, new trends in mathematics are emerging from the fruitful interaction between signal processing, image processing, and classical analysis. One example is given by ``wavelets'', which incorporate both the know-how of the Calderon-Zygmund school and the efficiency of some fast algorithms developed in signal processing (quadrature mirror filters and pyramidal algorithms.) A second example is ``multi-fractal analysis''. The initial motivation was the study of fully developed turbulence and the introduction by Frisch and Parisi of the multi-fractal spectrum. Multi-fractal analysis provides a deeper insight into many classical functions in mathematics. A third example--``chirps''--is studied in this book. Chirps are used in modern radar or sonar technology. Once given a precise mathematical definition, chirps constitute a powerful tool in classical analysis. In this book, wavelet analysis is related to the 2-microlocal spaces discovered by J. M. Bony. The authors then prove that a wavelet based multi-fractal analysis leads to a remarkable improvement of Sobolev embedding theorem. In addition, they show that chirps were hidden in a celebrated Riemann series. Features: Provides the reader with some basic training in new lines of research. Clarifies the relationship between pointwise behavior and size properties of wavelet coefficents.
Author : Stéphane Jaffard
Publisher : American Mathematical Soc.
ISBN 13 : 0821804758
Total Pages : 127 pages
Book Rating : 4.8/5 (218 download)
Download or read book Wavelet Methods for Pointwise Regularity and Local Oscillations of Functions written by Stéphane Jaffard and published by American Mathematical Soc.. This book was released on 1996 with total page 127 pages. Available in PDF, EPUB and Kindle. Book excerpt: We investigate several topics related to the local behavior of functions: pointwise Hölder regularity, local scaling invariance and very oscillatory "chirp-like" behaviors. Our main tool is to relate these notions to two-microlocal conditions which are defined either on the Littlewood-Paley decomposition or on the wavelet transform. We give characterizations and the main properties of these two-microlocal spaces and we give several applications, such as bounds on the dimension of the set of Hölder singularities of a function, Sobolev regularity of trace functions, and chirp expansions of specific functions.
Author : Alain Damlamian
Publisher : World Scientific
ISBN 13 : 9814464058
Total Pages : 190 pages
Book Rating : 4.8/5 (144 download)
Download or read book Wavelet Methods In Mathematical Analysis And Engineering written by Alain Damlamian and published by World Scientific. This book was released on 2010-09-21 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a comprehensive overview of both the fundamentals of wavelet analysis and related tools, and of the most active recent developments towards applications. It offers a state-of-the-art in several active areas of research where wavelet ideas, or more generally multiresolution ideas have proved particularly effective.The main applications covered are in the numerical analysis of PDEs, and signal and image processing. Recently introduced techniques such as Empirical Mode Decomposition (EMD) and new trends in the recovery of missing data, such as compressed sensing, are also presented. Applications range for the reconstruction of noisy or blurred images, pattern and face recognition, to nonlinear approximation in strongly anisotropic contexts, and to the classification tools based on multifractal analysis.
Author : Uwe Kähler
Publisher : Springer Nature
ISBN 13 : 3031363752
Total Pages : 696 pages
Book Rating : 4.0/5 (313 download)
Download or read book Analysis, Applications, and Computations written by Uwe Kähler and published by Springer Nature. This book was released on 2023-12-01 with total page 696 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the contributions of the participants of the 13th International ISAAC Congress 2021, held in Ghent, Belgium. The papers, written by respected international experts, address recent results in mathematics, with a special focus on analysis. The volume provides to both specialists and non-specialists an excellent source of information on current research in mathematical analysis and its various interdisciplinary applications.
Author : Patrice Abry
Publisher : John Wiley & Sons
ISBN 13 : 1118622901
Total Pages : 382 pages
Book Rating : 4.1/5 (186 download)
Download or read book Scaling, Fractals and Wavelets written by Patrice Abry and published by John Wiley & Sons. This book was released on 2013-03-01 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: Scaling is a mathematical transformation that enlarges or diminishes objects. The technique is used in a variety of areas, including finance and image processing. This book is organized around the notions of scaling phenomena and scale invariance. The various stochastic models commonly used to describe scaling — self-similarity, long-range dependence and multi-fractals — are introduced. These models are compared and related to one another. Next, fractional integration, a mathematical tool closely related to the notion of scale invariance, is discussed, and stochastic processes with prescribed scaling properties (self-similar processes, locally self-similar processes, fractionally filtered processes, iterated function systems) are defined. A number of applications where the scaling paradigm proved fruitful are detailed: image processing, financial and stock market fluctuations, geophysics, scale relativity, and fractal time-space.
Author : Michel Laurent Lapidus
Publisher : American Mathematical Soc.
ISBN 13 : 0821836382
Total Pages : 592 pages
Book Rating : 4.8/5 (218 download)
Download or read book Fractal Geometry and Applications: A Jubilee of Benoit Mandelbrot written by Michel Laurent Lapidus and published by American Mathematical Soc.. This book was released on 2004 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume offers an excellent selection of cutting-edge articles about fractal geometry, covering the great breadth of mathematics and related areas touched by this subject. Included are rich survey articles and fine expository papers. The high-quality contributions to the volume by well-known researchers--including two articles by Mandelbrot--provide a solid cross-section of recent research representing the richness and variety of contemporary advances in and around fractal geometry. In demonstrating the vitality and diversity of the field, this book will motivate further investigation into the many open problems and inspire future research directions. It is suitable for graduate students and researchers interested in fractal geometry and its applications. This is a two-part volume. Part 1 covers analysis, number theory, and dynamical systems; Part 2, multifractals, probability and statistical mechanics, and applications.
Author : Ayache Antoine
Publisher : World Scientific
ISBN 13 : 9814525677
Total Pages : 236 pages
Book Rating : 4.8/5 (145 download)
Download or read book Multifractional Stochastic Fields: Wavelet Strategies In Multifractional Frameworks written by Ayache Antoine and published by World Scientific. This book was released on 2018-09-24 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractional Brownian Motion (FBM) is a very classical continuous self-similar Gaussian field with stationary increments. In 1940, some works of Kolmogorov on turbulence led him to introduce this quite natural extension of Brownian Motion, which, in contrast with the latter, has correlated increments. However, the denomination FBM is due to a very famous article by Mandelbrot and Van Ness, published in 1968. Not only in it, but also in several of his following works, Mandelbrot emphasized the importance of FBM as a model in several applied areas, and thus he made it to be known by a wide community. Therefore, FBM has been studied by many authors, and used in a lot of applications.In spite of the fact that FBM is a very useful model, it does not always fit to real data. This is the reason why, for at least two decades, there has been an increasing interest in the construction of new classes of random models extending it, which offer more flexibility. A paradigmatic example of them is the class of Multifractional Fields. Multifractional means that fractal properties of models, typically, roughness of paths and self-similarity of probability distributions, are locally allowed to change from place to place.In order to sharply determine path behavior of Multifractional Fields, a wavelet strategy, which can be considered to be new in the probabilistic framework, has been developed since the end of the 90's. It is somehow inspired by some rather non-standard methods, related to the fine study of Brownian Motion roughness, through its representation in the Faber-Schauder system. The main goal of the book is to present the motivations behind this wavelet strategy, and to explain how it can be applied to some classical examples of Multifractional Fields. The book also discusses some topics concerning them which are not directly related to the wavelet strategy.
Author : Hans Triebel
Publisher : Springer Science & Business Media
ISBN 13 : 3764375825
Total Pages : 433 pages
Book Rating : 4.7/5 (643 download)
Download or read book Theory of Function Spaces III written by Hans Triebel and published by Springer Science & Business Media. This book was released on 2006-09-10 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the recent theory of function spaces, paying special attention to some recent developments related to neighboring areas such as numerics, signal processing, and fractal analysis. Local building blocks, in particular (non-smooth) atoms, quarks, wavelet bases and wavelet frames are considered in detail and applied to diverse problems, including a local smoothness theory, spaces on Lipschitz domains, and fractal analysis.
Download or read book Computation and Applied Mathematics written by and published by . This book was released on 1996 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Alain Vincent
Publisher : American Mathematical Soc.
ISBN 13 : 9780821808139
Total Pages : 220 pages
Book Rating : 4.8/5 (81 download)
Download or read book Numerical Methods in Fluid Mechanics written by Alain Vincent and published by American Mathematical Soc.. This book was released on 1998 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: At a level comprehensible to graduate students and beginning researchers, describes the state of the art in using numerical methods for analyzing turbulence in fluids, a problem still unsolved after centuries of research. The methods described include wavelet-based, semi-Lagrangian, Langrangian multi-pole, continuous adaptation of curvilinear grids, finite volume, and shock-capturing. Among the applications are industrial flows, aerodynamics, two-phase flows, astrophysical flows, and meteorology. Suitable as a course text for graduate students with a background in fluid mechanics. No index. Annotation copyrighted by Book News, Inc., Portland, OR
Author : Jan Felipe Van Diejen
Publisher : American Mathematical Soc.
ISBN 13 : 9780821873298
Total Pages : 302 pages
Book Rating : 4.8/5 (732 download)
Download or read book Algebraic Methods and Q-special Functions written by Jan Felipe Van Diejen and published by American Mathematical Soc.. This book was released on 1999-01-01 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: There has been revived interest in recent years in the study of special functions. Many of the latest advances in the field were inspired by the works of R. A. Askey and colleagues on basic hypergeometric series and I. G. Macdonald on orthogonal polynomials related to root systems. Significant progress was made by the use of algebraic techniques involving quantum groups, Hecke algebras, and combinatorial methods. The CRM organized a workshop for key researchers in the field to present an overview of current trends. This volume consists of the contributions to that workshop. Topics include basic hypergeometric functions, algebraic and representation-theoretic methods, combinatorics of symmetric functions, root systems, and the connections with integrable systems.
Author : Gary R. Jensen
Publisher : American Mathematical Soc.
ISBN 13 : 082183603X
Total Pages : 162 pages
Book Rating : 4.8/5 (218 download)
Download or read book 150 Years of Mathematics at Washington University in St. Louis written by Gary R. Jensen and published by American Mathematical Soc.. This book was released on 2006 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: Articles in this book are based on talks given at the conference commemorating the 150th anniversary of the Washington University in St. Louis. The articles cover a wide range of important topics in mathematics, and are written by former and present faculty or graduates of the Washington University Department of Mathematics. The volume is prefaced by a brief history of the Washington University Department of Mathematics, a roster of those who received the PhD degree from the department, and a list of the Washington University Department of Mathematics faculty.
Author : Syed Twareque Ali
Publisher : Springer Science & Business Media
ISBN 13 : 1461485355
Total Pages : 586 pages
Book Rating : 4.4/5 (614 download)
Download or read book Coherent States, Wavelets, and Their Generalizations written by Syed Twareque Ali and published by Springer Science & Business Media. This book was released on 2013-10-30 with total page 586 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second edition is fully updated, covering in particular new types of coherent states (the so-called Gazeau-Klauder coherent states, nonlinear coherent states, squeezed states, as used now routinely in quantum optics) and various generalizations of wavelets (wavelets on manifolds, curvelets, shearlets, etc.). In addition, it contains a new chapter on coherent state quantization and the related probabilistic aspects. As a survey of the theory of coherent states, wavelets, and some of their generalizations, it emphasizes mathematical principles, subsuming the theories of both wavelets and coherent states into a single analytic structure. The approach allows the user to take a classical-like view of quantum states in physics. Starting from the standard theory of coherent states over Lie groups, the authors generalize the formalism by associating coherent states to group representations that are square integrable over a homogeneous space; a further step allows one to dispense with the group context altogether. In this context, wavelets can be generated from coherent states of the affine group of the real line, and higher-dimensional wavelets arise from coherent states of other groups. The unified background makes transparent an entire range of properties of wavelets and coherent states. Many concrete examples, such as coherent states from semisimple Lie groups, Gazeau-Klauder coherent states, coherent states for the relativity groups, and several kinds of wavelets, are discussed in detail. The book concludes with a palette of potential applications, from the quantum physically oriented, like the quantum-classical transition or the construction of adequate states in quantum information, to the most innovative techniques to be used in data processing. Intended as an introduction to current research for graduate students and others entering the field, the mathematical discussion is self-contained. With its extensive references to the research literature, the first edition of the book is already a proven compendium for physicists and mathematicians active in the field, and with full coverage of the latest theory and results the revised second edition is even more valuable.
Author : Xingde Dai
Publisher : American Mathematical Soc.
ISBN 13 : 0821808001
Total Pages : 82 pages
Book Rating : 4.8/5 (218 download)
Download or read book Wandering Vectors for Unitary Systems and Orthogonal Wavelets written by Xingde Dai and published by American Mathematical Soc.. This book was released on 1998 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt: Investigates topological and structural properties of the set W(U) of all complete wandering vectors for a system U of unitary operators acting on a Hilbert space. The authors parameterize W(U) in terms of a fixed vector y and the set of all unitary operators which locally commute with U at y. No index. Annotation copyrighted by Book News, Inc., Portland, OR
Author : Maïtine Bergounioux
Publisher : Springer Science & Business Media
ISBN 13 : 3642196047
Total Pages : 203 pages
Book Rating : 4.6/5 (421 download)
Download or read book Mathematical Image Processing written by Maïtine Bergounioux and published by Springer Science & Business Media. This book was released on 2011-05-12 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: The contributions appearing in this volume are a snapshot of the different topics that were discussed during the Second Conference "Mathematics and Image Processing” held at the University of Orléans in 2010. They mainly concern, image reconstruction, texture extraction and image classification and involve a variety of different methods and applications. Therefore it was impossible to split the papers into generic groups which is why they are presented in alphabetic order. However they mainly concern: texture analysis (5 papers) with different techniques (variational analysis, wavelet and morphological component analysis, fractional Brownian fields), geometrical methods (2 papers ) for restoration and invariant feature detection, classification (with multifractal analysis), neurosciences imaging and analysis of Multi-Valued Images.
Author : Serge Dubuc
Publisher : American Mathematical Soc.
ISBN 13 : 9780821870181
Total Pages : 412 pages
Book Rating : 4.8/5 (71 download)
Download or read book Spline Functions and the Theory of Wavelets written by Serge Dubuc and published by American Mathematical Soc.. This book was released on 1999-01-01 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
