Harmonic Analysis And Fractal Analysis Over Local Fields And Applications
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Harmonic Analysis And Fractal Analysis Over Local Fields And Applications
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Author : Su Weiyi
language : en
Publisher: World Scientific
Release Date : 2017-08-17
Harmonic Analysis And Fractal Analysis Over Local Fields And Applications written by Su Weiyi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-17 with Mathematics categories.
This book is a monograph on harmonic analysis and fractal analysis over local fields. It can also be used as lecture notes/textbook or as recommended reading for courses on modern harmonic and fractal analysis. It is as reliable as Fourier Analysis on Local Fields published in 1975 which is regarded as the first monograph in this research field.The book is self-contained, with wide scope and deep knowledge, taking modern mathematics (such as modern algebra, point set topology, functional analysis, distribution theory, and so on) as bases. Specially, fractal analysis is studied in the viewpoint of local fields, and fractal calculus is established by pseudo-differential operators over local fields. A frame of fractal PDE is constructed based on fractal calculus instead of classical calculus. On the other hand, the author does his best to make those difficult concepts accessible to readers, illustrate clear comparison between harmonic analysis on Euclidean spaces and that on local fields, and at the same time provide motivations underlying the new concepts and techniques. Overall, it is a high quality, up to date and valuable book for interested readers.
Recent Developments In Fractals And Related Fields
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Author : Julien Barral
language : en
Publisher: Birkhäuser
Release Date : 2017-08-23
Recent Developments In Fractals And Related Fields written by Julien Barral and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-23 with Mathematics categories.
This contributed volume provides readers with an overview of the most recent developments in the mathematical fields related to fractals, including both original research contributions, as well as surveys from many of the leading experts on modern fractal theory and applications. It is an outgrowth of the Conference of Fractals and Related Fields III, that was held on September 19-25, 2015 in île de Porquerolles, France. Chapters cover fields related to fractals such as harmonic analysis, multifractal analysis, geometric measure theory, ergodic theory and dynamical systems, probability theory, number theory, wavelets, potential theory, partial differential equations, fractal tilings, combinatorics, and signal and image processing. The book is aimed at pure and applied mathematicians in these areas, as well as other researchers interested in discovering the fractal domain.
Recent Developments In Fractals And Related Fields
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Author : Julien Barral
language : en
Publisher: Birkhäuser
Release Date : 2010-08-12
Recent Developments In Fractals And Related Fields written by Julien Barral and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-08-12 with Mathematics categories.
The Applied and Numerical Harmonic Analysis (ANHA) book series aims to provide the engineering, mathematical, and scienti?c communities with s- ni?cant developments in harmonic analysis, ranging from abstract harmonic analysis to basic applications. The title of the series re?ects the importance of applications and numerical implementation, but richness and relevance of applications and implementation depend fundamentally on the structure and depth of theoretical underpinnings. Thus, from our point of view, the int- leaving of theory and applications and their creative symbiotic evolution is axiomatic. Harmonic analysis is a wellspring of ideas and applicability that has ?o- ished, developed, and deepened over time within many disciplines and by means of creative cross-fertilizationwith diverse areas. The intricate and f- damental relationship between harmonic analysis and ?elds such as signal processing, partial di?erential equations (PDEs), and image processing is - ?ected in our state-of-the-art ANHA series. Our vision of modern harmonic analysis includes mathematical areas such as wavelet theory, Banach algebras, classical Fourier analysis, time-frequency analysis, and fractal geometry, as well as the diverse topics that impinge on them.
Dyadic Walsh Analysis From 1924 Onwards Walsh Gibbs Butzer Dyadic Differentiation In Science Volume 2 Extensions And Generalizations
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Author : Radomir Stankovic
language : en
Publisher: Springer
Release Date : 2015-12-29
Dyadic Walsh Analysis From 1924 Onwards Walsh Gibbs Butzer Dyadic Differentiation In Science Volume 2 Extensions And Generalizations written by Radomir Stankovic and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-29 with Mathematics categories.
The second volume of the two volumes book is dedicated to various extensions and generalizations of Dyadic (Walsh) analysis and related applications. Considered are dyadic derivatives on Vilenkin groups and various other Abelian and finite non-Abelian groups. Since some important results were developed in former Soviet Union and China, we provide overviews of former work in these countries. Further, we present translations of three papers that were initially published in Chinese. The presentation continues with chapters written by experts in the area presenting discussions of applications of these results in specific tasks in the area of signal processing and system theory. Efficient computing of related differential operators on contemporary hardware, including graphics processing units, is also considered, which makes the methods and techniques of dyadic analysis and generalizations computationally feasible. The volume 2 of the book ends with a chapter presenting open problems pointed out by several experts in the area.
Harmonic Analysis And Applications
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Author : Christopher Heil
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-08-02
Harmonic Analysis And Applications written by Christopher Heil 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 2007-08-02 with Mathematics categories.
This self-contained volume in honor of John J. Benedetto covers a wide range of topics in harmonic analysis and related areas. These include weighted-norm inequalities, frame theory, wavelet theory, time-frequency analysis, and sampling theory. The chapters are clustered by topic to provide authoritative expositions that will be of lasting interest. The original papers collected are written by prominent researchers and professionals in the field. The book pays tribute to John J. Benedetto’s achievements and expresses an appreciation for the mathematical and personal inspiration he has given to so many students, co-authors, and colleagues.
Frontiers Of Fractal Analysis
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Author : Santo Banerjee
language : en
Publisher: CRC Press
Release Date : 2022-07-07
Frontiers Of Fractal Analysis written by Santo Banerjee and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-07-07 with Mathematics categories.
The history of describing natural objects using geometry is as old as the advent of science itself, in which traditional shapes are the basis of our intuitive understanding of geometry. However, nature is not restricted to such Euclidean objects which are only characterized typically by integer dimensions. Hence, the conventional geometric approach cannot meet the requirements of solving or analysing nonlinear problems which are related with natural phenomena, therefore, the fractal theory has been born, which aims to understand complexity and provide an innovative way to recognize irregularity and complex systems. Although the concepts of fractal geometry have found wide applications in many forefront areas of science, engineering and societal issues, they also have interesting implications of a more practical nature for the older classical areas of science. Since its discovery, there has been a surge of research activities in using this powerful concept in almost every branch of scientific disciplines to gain deep insights into many unresolved problems. This book includes eight chapters which focus on gathering cutting-edge research and proposing application of fractals features in both traditional scientific disciplines and in applied fields.
Wavelet Analysis On Local Fields Of Positive Characteristic
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Author : Biswaranjan Behera
language : en
Publisher: Springer Nature
Release Date : 2022-01-01
Wavelet Analysis On Local Fields Of Positive Characteristic written by Biswaranjan Behera and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-01 with Mathematics categories.
This book discusses the theory of wavelets on local fields of positive characteristic. The discussion starts with a thorough introduction to topological groups and local fields. It then provides a proof of the existence and uniqueness of Haar measures on locally compact groups. It later gives several examples of locally compact groups and describes their Haar measures. The book focuses on multiresolution analysis and wavelets on a local field of positive characteristic. It provides characterizations of various functions associated with wavelet analysis such as scaling functions, wavelets, MRA-wavelets and low-pass filters. Many other concepts which are discussed in details are biorthogonal wavelets, wavelet packets, affine and quasi-affine frames, MSF multiwavelets, multiwavelet sets, generalized scaling sets, scaling sets, unconditional basis properties of wavelets and shift invariant spaces.
New Trends In Applied Harmonic Analysis
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Author : Akram Aldroubi
language : en
Publisher: Birkhäuser
Release Date : 2016-04-21
New Trends In Applied Harmonic Analysis written by Akram Aldroubi and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-21 with Mathematics categories.
This volume is a selection of written notes corresponding to courses taught at the CIMPA School: "New Trends in Applied Harmonic Analysis: Sparse Representations, Compressed Sensing and Multifractal Analysis". New interactions between harmonic analysis and signal and image processing have seen striking development in the last 10 years, and several technological deadlocks have been solved through the resolution of deep theoretical problems in harmonic analysis. New Trends in Applied Harmonic Analysis focuses on two particularly active areas that are representative of such advances: multifractal analysis, and sparse representation and compressed sensing. The contributions are written by leaders in these areas, and cover both theoretical aspects and applications. This work should prove useful not only to PhD students and postdocs in mathematics and signal and image processing, but also to researchers working in related topics.
Fractal Functions Fractal Surfaces And Wavelets
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Author : Peter R. Massopust
language : en
Publisher: Academic Press
Release Date : 2016-09-02
Fractal Functions Fractal Surfaces And Wavelets written by Peter R. Massopust and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-02 with Mathematics categories.
Fractal Functions, Fractal Surfaces, and Wavelets, Second Edition, is the first systematic exposition of the theory of local iterated function systems, local fractal functions and fractal surfaces, and their connections to wavelets and wavelet sets. The book is based on Massopust’s work on and contributions to the theory of fractal interpolation, and the author uses a number of tools—including analysis, topology, algebra, and probability theory—to introduce readers to this exciting subject. Though much of the material presented in this book is relatively current (developed in the past decades by the author and his colleagues) and fairly specialized, an informative background is provided for those entering the field. With its coherent and comprehensive presentation of the theory of univariate and multivariate fractal interpolation, this book will appeal to mathematicians as well as to applied scientists in the fields of physics, engineering, biomathematics, and computer science. In this second edition, Massopust includes pertinent application examples, further discusses local IFS and new fractal interpolation or fractal data, further develops the connections to wavelets and wavelet sets, and deepens and extends the pedagogical content. Offers a comprehensive presentation of fractal functions and fractal surfaces Includes latest developments in fractal interpolation Connects fractal geometry with wavelet theory Includes pertinent application examples, further discusses local IFS and new fractal interpolation or fractal data, and further develops the connections to wavelets and wavelet sets Deepens and extends the pedagogical content
Fractal Analysis
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Author : Sid-Ali Ouadfeul
language : en
Publisher: BoD – Books on Demand
Release Date : 2019-04-03
Fractal Analysis written by Sid-Ali Ouadfeul and has been published by BoD – Books on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-03 with Mathematics categories.
The aim of this book is to show some applications of fractal analysis in the fields of sciences. The first chapter introduces the readers to the book, while the second chapter shows the methods and challenges of fractal analysis of time-series data sets. The third chapter demonstrates fractal geometry as an attractive choice for miniaturized planar microwave filter design. The fourth chapter presents fractal antennas for wearable applications. The objective of the fifth chapter is to show some Parrondian games in discrete dynamic systems, while the last chapter reveals fractal structures of carbon nanotube system arrays.