Harmonic Analysis And Fractal Analysis Over Local Fields And Applications

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Harmonic Analysis And Fractal Analysis Over Local Fields And Applications

Su Weiyi
Harmonic Analysis And Fractal Analysis Over Local Fields And Applications Book PDF

Author : Su Weiyi
Publisher : World Scientific
Page : 332 pages
File Size : 44,6 Mb
Release : 2017-08-17
Category : Mathematics
ISBN : 9789813200524

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Harmonic Analysis And Fractal Analysis Over Local Fields And Applications by Su Weiyi Pdf

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

Julien Barral,Stéphane Seuret
Recent Developments in Fractals and Related Fields Book PDF

Author : Julien Barral,Stéphane Seuret
Publisher : Birkhäuser
Page : 312 pages
File Size : 47,7 Mb
Release : 2017-08-23
Category : Mathematics
ISBN : 9783319578057

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Recent Developments in Fractals and Related Fields by Julien Barral,Stéphane Seuret Pdf

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

Julien Barral,Stéphane Seuret
Recent Developments in Fractals and Related Fields Book PDF

Author : Julien Barral,Stéphane Seuret
Publisher : Birkhäuser
Page : 419 pages
File Size : 43,9 Mb
Release : 2010-08-12
Category : Mathematics
ISBN : 0817648879

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Recent Developments in Fractals and Related Fields by Julien Barral,Stéphane Seuret Pdf

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

Radomir Stankovic,Paul Leo Butzer,Ferenc Schipp,William R. Wade,Weiyi Su,Yasushi Endow,Sandor Fridli,Boris I. Golubov,Franz Pichler
Dyadic Walsh Analysis from 1924 Onwards Walsh Gibbs Butzer Dyadic Differentiation in Science Volume 2 Extensions and Generalizations Book PDF

Author : Radomir Stankovic,Paul Leo Butzer,Ferenc Schipp,William R. Wade,Weiyi Su,Yasushi Endow,Sandor Fridli,Boris I. Golubov,Franz Pichler
Publisher : Springer
Page : 360 pages
File Size : 49,8 Mb
Release : 2015-12-29
Category : Mathematics
ISBN : 9789462391635

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Dyadic Walsh Analysis from 1924 Onwards Walsh-Gibbs-Butzer Dyadic Differentiation in Science Volume 2 Extensions and Generalizations by Radomir Stankovic,Paul Leo Butzer,Ferenc Schipp,William R. Wade,Weiyi Su,Yasushi Endow,Sandor Fridli,Boris I. Golubov,Franz Pichler Pdf

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.

Wavelet Analysis on Local Fields of Positive Characteristic

Biswaranjan Behera,Qaiser Jahan
Wavelet Analysis on Local Fields of Positive Characteristic Book PDF

Author : Biswaranjan Behera,Qaiser Jahan
Publisher : Springer Nature
Page : 345 pages
File Size : 50,5 Mb
Release : 2022-01-01
Category : Mathematics
ISBN : 9789811678813

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Wavelet Analysis on Local Fields of Positive Characteristic by Biswaranjan Behera,Qaiser Jahan Pdf

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.

Harmonic Analysis and Applications

Christopher Heil
Harmonic Analysis and Applications Book PDF

Author : Christopher Heil
Publisher : Springer Science & Business Media
Page : 390 pages
File Size : 49,5 Mb
Release : 2007-08-02
Category : Mathematics
ISBN : 9780817645045

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Harmonic Analysis and Applications by Christopher Heil Pdf

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.

Difference Equations, Discrete Dynamical Systems and Applications

Martin Bohner,Yiming Ding,Ondřej Došlý
Difference Equations Discrete Dynamical Systems and Applications Book PDF

Author : Martin Bohner,Yiming Ding,Ondřej Došlý
Publisher : Springer
Page : 195 pages
File Size : 46,8 Mb
Release : 2015-12-01
Category : Mathematics
ISBN : 9783319247472

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Difference Equations, Discrete Dynamical Systems and Applications by Martin Bohner,Yiming Ding,Ondřej Došlý Pdf

These proceedings of the 20th International Conference on Difference Equations and Applications cover the areas of difference equations, discrete dynamical systems, fractal geometry, difference equations and biomedical models, and discrete models in the natural sciences, social sciences and engineering. The conference was held at the Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences (Hubei, China), under the auspices of the International Society of Difference Equations (ISDE) in July 2014. Its purpose was to bring together renowned researchers working actively in the respective fields, to discuss the latest developments, and to promote international cooperation on the theory and applications of difference equations. This book will appeal to researchers and scientists working in the fields of difference equations, discrete dynamical systems and their applications.

New Trends in Applied Harmonic Analysis

Akram Aldroubi,Carlos Cabrelli,Stephane Jaffard,Ursula Molter
New Trends in Applied Harmonic Analysis Book PDF

Author : Akram Aldroubi,Carlos Cabrelli,Stephane Jaffard,Ursula Molter
Publisher : Birkhäuser
Page : 334 pages
File Size : 52,5 Mb
Release : 2016-04-21
Category : Mathematics
ISBN : 9783319278735

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New Trends in Applied Harmonic Analysis by Akram Aldroubi,Carlos Cabrelli,Stephane Jaffard,Ursula Molter Pdf

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.

Frontiers of Fractal Analysis

Santo Banerjee,A. Gowrisankar
Frontiers of Fractal Analysis Book PDF

Author : Santo Banerjee,A. Gowrisankar
Publisher : CRC Press
Page : 182 pages
File Size : 44,6 Mb
Release : 2022-07-07
Category : Mathematics
ISBN : 9781000625875

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Frontiers of Fractal Analysis by Santo Banerjee,A. Gowrisankar Pdf

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.

New Trends in Applied Harmonic Analysis, Volume 2

Akram Aldroubi,Carlos Cabrelli,Stéphane Jaffard,Ursula Molter
New Trends in Applied Harmonic Analysis Volume 2 Book PDF

Author : Akram Aldroubi,Carlos Cabrelli,Stéphane Jaffard,Ursula Molter
Publisher : Springer Nature
Page : 335 pages
File Size : 49,8 Mb
Release : 2019-11-26
Category : Mathematics
ISBN : 9783030323530

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New Trends in Applied Harmonic Analysis, Volume 2 by Akram Aldroubi,Carlos Cabrelli,Stéphane Jaffard,Ursula Molter Pdf

This contributed volume collects papers based on courses and talks given at the 2017 CIMPA school Harmonic Analysis, Geometric Measure Theory and Applications, which took place at the University of Buenos Aires in August 2017. These articles highlight recent breakthroughs in both harmonic analysis and geometric measure theory, particularly focusing on their impact on image and signal processing. The wide range of expertise present in these articles will help readers contextualize how these breakthroughs have been instrumental in resolving deep theoretical problems. Some topics covered include: Gabor frames Falconer distance problem Hausdorff dimension Sparse inequalities Fractional Brownian motion Fourier analysis in geometric measure theory This volume is ideal for applied and pure mathematicians interested in the areas of image and signal processing. Electrical engineers and statisticians studying these fields will also find this to be a valuable resource.

Further Developments in Fractals and Related Fields

Julien Barral,Stéphane Seuret
Further Developments in Fractals and Related Fields Book PDF

Author : Julien Barral,Stéphane Seuret
Publisher : Birkhäuser
Page : 288 pages
File Size : 45,8 Mb
Release : 2013-02-20
Category : Mathematics
ISBN : 0817684018

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Further Developments in Fractals and Related Fields by Julien Barral,Stéphane Seuret Pdf

This volume, following in the tradition of a similar 2010 publication by the same editors, is an outgrowth of an international conference, “Fractals and Related Fields II,” held in June 2011. The book provides readers with an overview of developments in the mathematical fields related to fractals, including original research contributions as well as surveys from many of the leading experts on modern fractal theory and applications. The chapters cover fields related to fractals such as: *geometric measure theory *ergodic theory *dynamical systems *harmonic and functional analysis *number theory *probability theory Further Developments in Fractals and Related Fields is aimed at pure and applied mathematicians working in the above-mentioned areas as well as other researchers interested in discovering the fractal domain. Throughout the volume, readers will find interesting and motivating results as well as new avenues for further research.

Fractal Functions, Fractal Surfaces, and Wavelets

Peter R. Massopust
Fractal Functions Fractal Surfaces and Wavelets Book PDF

Author : Peter R. Massopust
Publisher : Academic Press
Page : 426 pages
File Size : 47,8 Mb
Release : 2016-09-02
Category : Mathematics
ISBN : 9780128044704

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Fractal Functions, Fractal Surfaces, and Wavelets by Peter R. Massopust Pdf

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

Fernando Brambila
Fractal Analysis Book PDF

Author : Fernando Brambila
Publisher : BoD – Books on Demand
Page : 296 pages
File Size : 43,6 Mb
Release : 2017-06-14
Category : Mathematics
ISBN : 9789535131915

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Fractal Analysis by Fernando Brambila Pdf

Fractal analysis has entered a new era. The applications to different areas of knowledge have been surprising. Let us begin with the fractional calculus-fractal geometry relationship, which allows for modeling with extreme precision of phenomena such as diffusion in porous media with fractional partial differential equations in fractal objects. Where the order of the equation is the same as the fractal dimension, this allows us to make calculations with enormous precision in diffusion phenomena-particularly in the oil industry, for new spillage prevention. Main applications to industry, design of fractal antennas to receive all frequencies and that is used in all cell phones, spacecraft, radars, image processing, measure, porosity, turbulence, scattering theory. Benoit Mandelbrot, creator of fractal geometry, would have been surprised by the use of fractal analysis presented in this book: "Part I: Petroleum Industry and Numerical Analysis"; "Part II: Fractal Antennas, Spacecraft, Radars, Image Processing, and Measure"; and "Part III: Scattering Theory, Porosity, and Turbulence." It's impossible to picture today's research without fractal analysis.

Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics: Fractals in pure mathematics

David Carfi,Michel Laurent Lapidus,Erin P. J. Pearse,Machiel Van Frankenhuysen
Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics Fractals in pure mathematics Book PDF

Author : David Carfi,Michel Laurent Lapidus,Erin P. J. Pearse,Machiel Van Frankenhuysen
Publisher : American Mathematical Soc.
Page : 410 pages
File Size : 47,7 Mb
Release : 2013-10-22
Category : Mathematics
ISBN : 9780821891476

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Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics: Fractals in pure mathematics by David Carfi,Michel Laurent Lapidus,Erin P. J. Pearse,Machiel Van Frankenhuysen Pdf

This volume contains the proceedings from three conferences: the PISRS 2011 International Conference on Analysis, Fractal Geometry, Dynamical Systems and Economics, held November 8-12, 2011 in Messina, Italy; the AMS Special Session on Fractal Geometry in Pure and Applied Mathematics, in memory of Benoit Mandelbrot, held January 4-7, 2012, in Boston, MA; and the AMS Special Session on Geometry and Analysis on Fractal Spaces, held March 3-4, 2012, in Honolulu, HI. Articles in this volume cover fractal geometry (and some aspects of dynamical systems) in pure mathematics. Also included are articles discussing a variety of connections of fractal geometry with other fields of mathematics, including probability theory, number theory, geometric measure theory, partial differential equations, global analysis on non-smooth spaces, harmonic analysis and spectral geometry. The companion volume (Contemporary Mathematics, Volume 601) focuses on applications of fractal geometry and dynamical systems to other sciences, including physics, engineering, computer science, economics, and finance.

Wavelets and Multiscale Analysis

Jonathan Cohen,Ahmed I. Zayed
Wavelets and Multiscale Analysis Book PDF

Author : Jonathan Cohen,Ahmed I. Zayed
Publisher : Springer Science & Business Media
Page : 338 pages
File Size : 42,6 Mb
Release : 2011-03-01
Category : Mathematics
ISBN : 9780817680954

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Wavelets and Multiscale Analysis by Jonathan Cohen,Ahmed I. Zayed Pdf

Since its emergence as an important research area in the early 1980s, the topic of wavelets has undergone tremendous development on both theoretical and applied fronts. Myriad research and survey papers and monographs have been published on the subject, documenting different areas of applications such as sound and image processing, denoising, data compression, tomography, and medical imaging. The study of wavelets remains a very active field of research, and many of its central techniques and ideas have evolved into new and promising research areas. This volume, a collection of invited contributions developed from talks at an international conference on wavelets, is divided into three parts: Part I is devoted to the mathematical theory of wavelets and features several papers on wavelet sets and the construction of wavelet bases in different settings. Part II looks at the use of multiscale harmonic analysis for understanding the geometry of large data sets and extracting information from them. Part III focuses on applications of wavelet theory to the study of several real-world problems. Overall, the book is an excellent reference for graduate students, researchers, and practitioners in theoretical and applied mathematics, or in engineering.