Wavelet Methods For Pointwise Regularity And Local Oscillations Of Functions
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Wavelet Methods For Pointwise Regularity And Local Oscillations Of Functions
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Author : Stéphane Jaffard
language : en
Publisher: American Mathematical Soc.
Release Date : 1996
Wavelet Methods For Pointwise Regularity And Local Oscillations Of Functions written by Stéphane Jaffard and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Mathematics categories.
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.
Wavelet Methods In Mathematical Analysis And Engineering
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Author : Alain Damlamian
language : en
Publisher: World Scientific
Release Date : 2010-09-21
Wavelet Methods In Mathematical Analysis And Engineering written by Alain Damlamian and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-09-21 with Mathematics categories.
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.
Fractals Theory And Applications In Engineering
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Author : Michel Dekking
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Fractals Theory And Applications In Engineering written by Michel Dekking and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Technology & Engineering categories.
Owing to the rapid emergence and growth of techniques in the engineering application of fractals, it has become necessary to gather the most recent advances on a regular basis. This book is a continuation of the first volume - published in 1997 - but contains interesting developments. A major point is that mathematics has become more and more involved in the definition and use of fractal models. It seems that the time of the qualitative observation of fractal phenomena has gone. Now the main models are strongly based upon theoretical arguments. Fractals: Theory and Applications in Engineering is a multidisciplinary book which should interest every scientist working in areas connected to fractals.
An Invitation To Fractal Geometry
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Author : Michel L. Lapidus
language : en
Publisher: American Mathematical Society
Release Date : 2024-12-30
An Invitation To Fractal Geometry written by Michel L. Lapidus and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-30 with Mathematics categories.
This book offers a comprehensive exploration of fractal dimensions, self-similarity, and fractal curves. Aimed at undergraduate and graduate students, postdocs, mathematicians, and scientists across disciplines, this text requires minimal prerequisites beyond a solid foundation in undergraduate mathematics. While fractal geometry may seem esoteric, this book demystifies it by providing a thorough introduction to its mathematical underpinnings and applications. Complete proofs are provided for most of the key results, and exercises of different levels of difficulty are proposed throughout the book. Key topics covered include the Hausdorff metric, Hausdorff measure, and fractal dimensions such as Hausdorff and Minkowski dimensions. The text meticulously constructs and analyzes Hausdorff measure, offering readers a deep understanding of its properties. Through emblematic examples like the Cantor set, the Sierpinski gasket, the Koch snowflake curve, and the Weierstrass curve, readers are introduced to self-similar sets and their construction via the iteration of contraction mappings. The book also sets the stage for the advanced theory of complex dimensions and fractal drums by gently introducing it via a variety of classical examples, including well-known fractal curves. By intertwining historical context with rigorous mathematical exposition, this book serves as both a stand-alone resource and a gateway to deeper explorations in fractal geometry.
Wavelet Methods For Pointwise Regularity And Local Oscillations Of Functions
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Author : Stéphane Jaffard
language : en
Publisher:
Release Date : 1996
Wavelet Methods For Pointwise Regularity And Local Oscillations Of Functions written by Stéphane Jaffard and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Littlewood-Paley theory categories.
Wavelet Transforms And Their Applications
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Author : Lokenath Debnath
language : en
Publisher: Springer
Release Date : 2014-11-25
Wavelet Transforms And Their Applications written by Lokenath Debnath and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-25 with Technology & Engineering categories.
This textbook is an introduction to wavelet transforms and accessible to a larger audience with diverse backgrounds and interests in mathematics, science, and engineering. Emphasis is placed on the logical development of fundamental ideas and systematic treatment of wavelet analysis and its applications to a wide variety of problems as encountered in various interdisciplinary areas. Topics and Features: * This second edition heavily reworks the chapters on Extensions of Multiresolution Analysis and Newlands’s Harmonic Wavelets and introduces a new chapter containing new applications of wavelet transforms * Uses knowledge of Fourier transforms, some elementary ideas of Hilbert spaces, and orthonormal systems to develop the theory and applications of wavelet analysis * Offers detailed and clear explanations of every concept and method, accompanied by carefully selected worked examples, with special emphasis given to those topics in which students typically experience difficulty * Includes carefully chosen end-of-chapter exercises directly associated with applications or formulated in terms of the mathematical, physical, and engineering context and provides answers to selected exercises for additional help Mathematicians, physicists, computer engineers, and electrical and mechanical engineers will find Wavelet Transforms and Their Applications an exceptionally complete and accessible text and reference. It is also suitable as a self-study or reference guide for practitioners and professionals.
Probability In Complex Physical Systems
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Author : Jean-Dominique Deuschel
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-04-23
Probability In Complex Physical Systems written by Jean-Dominique Deuschel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-23 with Mathematics categories.
Probabilistic approaches have played a prominent role in the study of complex physical systems for more than thirty years. This volume collects twenty articles on various topics in this field, including self-interacting random walks and polymer models in random and non-random environments, branching processes, Parisi formulas and metastability in spin glasses, and hydrodynamic limits for gradient Gibbs models. The majority of these articles contain original results at the forefront of contemporary research; some of them include review aspects and summarize the state-of-the-art on topical issues – one focal point is the parabolic Anderson model, which is considered with various novel aspects including moving catalysts, acceleration and deceleration and fron propagation, for both time-dependent and time-independent potentials. The authors are among the world’s leading experts. This Festschrift honours two eminent researchers, Erwin Bolthausen and Jürgen Gärtner, whose scientific work has profoundly influenced the field and all of the present contributions.
Analysis And Probability
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Author : Palle E. T. Jorgensen
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-10-17
Analysis And Probability written by Palle E. T. Jorgensen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-10-17 with Mathematics categories.
If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is. —John von Neumann While this is a course in analysis, our approach departs from the beaten path in some ways. Firstly, we emphasize a variety of connections to themes from neighboring fields, such as wavelets, fractals and signals; topics typically not included in a gradu ate analysis course. This in turn entails excursions into domains with a probabilistic flavor. Yet the diverse parts of the book follow a common underlying thread, and to gether they constitute a good blend; each part in the mix naturally complements the other. In fact, there are now good reasons for taking a wider view of analysis, for ex ample the fact that several applied trends have come to interact in new and exciting ways with traditional mathematical analysis—as it was taught in graduate classes for generations. One consequence of these impulses from "outside" is that conventional boundaries between core disciplines in mathematics have become more blurred. Fortunately this branching out does not mean that students will need to start out with any different or additional prerequisites. In fact, the ideas involved in this book are intuitive, natural, many of them visual, and geometric. The required background is quite minimal and it does not go beyond what is typically required in most graduate programs.
A Wavelet Tour Of Signal Processing
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Author : Stephane Mallat
language : en
Publisher: Elsevier
Release Date : 1999-09-14
A Wavelet Tour Of Signal Processing written by Stephane Mallat and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-09-14 with Computers categories.
This book is intended to serve as an invaluable reference for anyone concerned with the application of wavelets to signal processing. It has evolved from material used to teach "wavelet signal processing" courses in electrical engineering departments at Massachusetts Institute of Technology and Tel Aviv University, as well as applied mathematics departments at the Courant Institute of New York University and ÉcolePolytechnique in Paris. - Provides a broad perspective on the principles and applications of transient signal processing with wavelets - Emphasizes intuitive understanding, while providing the mathematical foundations and description of fast algorithms - Numerous examples of real applications to noise removal, deconvolution, audio and image compression, singularity and edge detection, multifractal analysis, and time-varying frequency measurements - Algorithms and numerical examples are implemented in Wavelab, which is a Matlab toolbox freely available over the Internet - Content is accessible on several level of complexity, depending on the individual reader's needs New to the Second Edition - Optical flow calculation and video compression algorithms - Image models with bounded variation functions - Bayes and Minimax theories for signal estimation - 200 pages rewritten and most illustrations redrawn - More problems and topics for a graduate course in wavelet signal processing, in engineering and applied mathematics
L Functions For The Orthogonal Group
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Author : David Ginzburg
language : en
Publisher: American Mathematical Soc.
Release Date : 1997
L Functions For The Orthogonal Group written by David Ginzburg and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.
In this book, the authors establish global Rankin Selberg integrals which determine the standard [italic capital]L function for the group [italic capitals]GL[subscript italic]r x [italic capital]Gʹ, where [italic capital]Gʹ is an isometry group of a nondegenerate symmetric form. The class of automorphic representations considered here is for any pair [capital Greek]Pi1 [otimes/dyadic/Kronecker/tensor product symbol] [capital Greek]Pi2 where [capital Greek]Pi1 is generic cuspidal for [italic capitals]GL[subscript italic]r([italic capital]A) and [capital Greek]Pi2 is cuspidal for [italic capital]Gʹ([italic capital]A). The construction of these [italic capital]L functions involves the use of certain new "models" of local representations; these models generalize the usual generic models. The authors also computer local unramified factors in a new way using geometric ideas.