Trends In Harmonic Analysis And Its Applications

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Trends in Harmonic Analysis and Its Applications

Author : Jens G. Christensen
Publisher : American Mathematical Soc.
ISBN 13 : 1470418797
Total Pages : 218 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Trends in Harmonic Analysis and Its Applications by : Jens G. Christensen

Download or read book Trends in Harmonic Analysis and Its Applications written by Jens G. Christensen and published by American Mathematical Soc.. This book was released on 2015-10-27 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the AMS Special Session on Harmonic Analysis and Its Applications held March 29-30, 2014, at the University of Maryland, Baltimore County, Baltimore, MD. It provides an in depth look at the many directions taken by experts in Harmonic Analysis and related areas. The papers cover topics such as frame theory, Gabor analysis, interpolation and Besov spaces on compact manifolds, Cuntz-Krieger algebras, reproducing kernel spaces, solenoids, hypergeometric shift operators and analysis on infinite dimensional groups. Expositions are by leading researchers in the field, both young and established. The papers consist of new results or new approaches to solutions, and at the same time provide an introduction into the respective subjects.

Harmonic Analysis and Applications

Author : John J. Benedetto
Publisher : CRC Press
ISBN 13 : 1000142213
Total Pages : 370 pages
Book Rating : 4.0/5 (1 download)

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Book Synopsis Harmonic Analysis and Applications by : John J. Benedetto

Download or read book Harmonic Analysis and Applications written by John J. Benedetto and published by CRC Press. This book was released on 2020-12-18 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: Harmonic analysis plays an essential role in understanding a host of engineering, mathematical, and scientific ideas. In Harmonic Analysis and Applications, the analysis and synthesis of functions in terms of harmonics is presented in such a way as to demonstrate the vitality, power, elegance, usefulness, and the intricacy and simplicity of the subject. This book is about classical harmonic analysis - a textbook suitable for students, and an essay and general reference suitable for mathematicians, physicists, and others who use harmonic analysis. Throughout the book, material is provided for an upper level undergraduate course in harmonic analysis and some of its applications. In addition, the advanced material in Harmonic Analysis and Applications is well-suited for graduate courses. The course is outlined in Prologue I. This course material is excellent, not only for students, but also for scientists, mathematicians, and engineers as a general reference. Chapter 1 covers the Fourier analysis of integrable and square integrable (finite energy) functions on R. Chapter 2 of the text covers distribution theory, emphasizing the theory's useful vantage point for dealing with problems and general concepts from engineering, physics, and mathematics. Chapter 3 deals with Fourier series, including the Fourier analysis of finite and infinite sequences, as well as functions defined on finite intervals. The mathematical presentation, insightful perspectives, and numerous well-chosen examples and exercises in Harmonic Analysis and Applications make this book well worth having in your collection.

Recent Developments in Harmonic Analysis and its Applications

Author : Shaoming Guo
Publisher : American Mathematical Society
ISBN 13 : 147047140X
Total Pages : 182 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Recent Developments in Harmonic Analysis and its Applications by : Shaoming Guo

Download or read book Recent Developments in Harmonic Analysis and its Applications written by Shaoming Guo and published by American Mathematical Society. This book was released on 2024-01-24 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the virtual AMS Special Session on Harmonic Analysis, held from March 26–27, 2022. Harmonic analysis has gone through rapid developments in the past decade. New tools, including multilinear Kakeya inequalities, broad-narrow analysis, polynomial methods, decoupling inequalities, and refined Strichartz inequalities, are playing a crucial role in resolving problems that were previously considered out of reach. A large number of important works in connection with geometric measure theory, analytic number theory, partial differential equations, several complex variables, etc., have appeared in the last few years. This book collects some examples of this work.

New Trends in Applied Harmonic Analysis, Volume 2

Author : Akram Aldroubi
Publisher : Springer Nature
ISBN 13 : 3030323536
Total Pages : 335 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis New Trends in Applied Harmonic Analysis, Volume 2 by : Akram Aldroubi

Download or read book New Trends in Applied Harmonic Analysis, Volume 2 written by Akram Aldroubi and published by Springer Nature. This book was released on 2019-11-26 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Harmonic Analysis and Applications

Author : Carlos E. Kenig
Publisher : American Mathematical Soc.
ISBN 13 : 1470461277
Total Pages : 345 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Harmonic Analysis and Applications by : Carlos E. Kenig

Download or read book Harmonic Analysis and Applications written by Carlos E. Kenig and published by American Mathematical Soc.. This book was released on 2020-12-14 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: The origins of the harmonic analysis go back to an ingenious idea of Fourier that any reasonable function can be represented as an infinite linear combination of sines and cosines. Today's harmonic analysis incorporates the elements of geometric measure theory, number theory, probability, and has countless applications from data analysis to image recognition and from the study of sound and vibrations to the cutting edge of contemporary physics. The present volume is based on lectures presented at the summer school on Harmonic Analysis. These notes give fresh, concise, and high-level introductions to recent developments in the field, often with new arguments not found elsewhere. The volume will be of use both to graduate students seeking to enter the field and to senior researchers wishing to keep up with current developments.

Recent Developments in Harmonic Analysis and Its Applications

Author : Shaoming Guo
Publisher :
ISBN 13 : 9781470471408
Total Pages : 0 pages
Book Rating : 4.4/5 (714 download)

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Book Synopsis Recent Developments in Harmonic Analysis and Its Applications by : Shaoming Guo

Download or read book Recent Developments in Harmonic Analysis and Its Applications written by Shaoming Guo and published by . This book was released on 2024 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Evolution of Applied Harmonic Analysis

Author : Elena Prestini
Publisher : Birkhäuser
ISBN 13 : 1489979891
Total Pages : 377 pages
Book Rating : 4.4/5 (899 download)

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Book Synopsis The Evolution of Applied Harmonic Analysis by : Elena Prestini

Download or read book The Evolution of Applied Harmonic Analysis written by Elena Prestini and published by Birkhäuser. This book was released on 2016-12-01 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: A sweeping exploration of the development and far-reaching applications of harmonic analysis such as signal processing, digital music, Fourier optics, radio astronomy, crystallography, medical imaging, spectroscopy, and more. Featuring a wealth of illustrations, examples, and material not found in other harmonic analysis books, this unique monograph skillfully blends together historical narrative with scientific exposition to create a comprehensive yet accessible work. While only an understanding of calculus is required to appreciate it, there are more technical sections that will charm even specialists in harmonic analysis. From undergraduates to professional scientists, engineers, and mathematicians, there is something for everyone here. The second edition of The Evolution of Applied Harmonic Analysis contains a new chapter on atmospheric physics and climate change, making it more relevant for today’s audience. Praise for the first edition: "...can be thoroughly recommended to any reader who is curious about the physical world and the intellectual underpinnings that have lead to our expanding understanding of our physical environment and to our halting steps to control it. Everyone who uses instruments that are based on harmonic analysis will benefit from the clear verbal descriptions that are supplied." — R.N. Bracewell, Stanford University “The book under review is a unique and splendid telling of the triumphs of the fast Fourier transform. I can recommend it unconditionally... Elena Prestini... has taken one major mathematical idea, that of Fourier analysis, and chased down and described a half dozen varied areas in which Fourier analysis and the FFT are now in place. Her book is much to be applauded.” — Society for Industrial and Applied Mathematics “This is not simply a book about mathematics, or even the history of mathematics; it is a story about how the discipline has been applied (to borrow Fourier’s expression) to ‘the public good and the explanation of natural phenomena.’ ... This book constitutes a significant addition to the library of popular mathematical works, and a valuable resource for students of mathematics.” — Mathematical Association of America Reviews

Trends in Harmonic Analysis

Author : Massimo A. Picardello
Publisher : Springer Science & Business Media
ISBN 13 : 8847028531
Total Pages : 450 pages
Book Rating : 4.8/5 (47 download)

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Book Synopsis Trends in Harmonic Analysis by : Massimo A. Picardello

Download or read book Trends in Harmonic Analysis written by Massimo A. Picardello and published by Springer Science & Business Media. This book was released on 2012-12-05 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book illustrates the wide range of research subjects developed by the Italian research group in harmonic analysis, originally started by Alessandro Figà-Talamanca, to whom it is dedicated in the occasion of his retirement. In particular, it outlines some of the impressive ramifications of the mathematical developments that began when Figà-Talamanca brought the study of harmonic analysis to Italy; the research group that he nurtured has now expanded to cover many areas. Therefore the book is addressed not only to experts in harmonic analysis, summability of Fourier series and singular integrals, but also in potential theory, symmetric spaces, analysis and partial differential equations on Riemannian manifolds, analysis on graphs, trees, buildings and discrete groups, Lie groups and Lie algebras, and even in far-reaching applications as for instance cellular automata and signal processing (low-discrepancy sampling, Gaussian noise).

Operator Theory and Harmonic Analysis

Author : Alexey N. Karapetyants
Publisher : Springer Nature
ISBN 13 : 3030774937
Total Pages : 585 pages
Book Rating : 4.0/5 (37 download)

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Book Synopsis Operator Theory and Harmonic Analysis by : Alexey N. Karapetyants

Download or read book Operator Theory and Harmonic Analysis written by Alexey N. Karapetyants and published by Springer Nature. This book was released on 2021-09-27 with total page 585 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is part of the collaboration agreement between Springer and the ISAAC society. This is the first in the two-volume series originating from the 2020 activities within the international scientific conference "Modern Methods, Problems and Applications of Operator Theory and Harmonic Analysis" (OTHA), Southern Federal University in Rostov-on-Don, Russia. This volume is focused on general harmonic analysis and its numerous applications. The two volumes cover new trends and advances in several very important fields of mathematics, developed intensively over the last decade. The relevance of this topic is related to the study of complex multiparameter objects required when considering operators and objects with variable parameters.

New Trends in Applied Harmonic Analysis

Author : Akram Aldroubi
Publisher : Birkhäuser
ISBN 13 : 3319278738
Total Pages : 356 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis New Trends in Applied Harmonic Analysis by : Akram Aldroubi

Download or read book New Trends in Applied Harmonic Analysis written by Akram Aldroubi and published by Birkhäuser. This book was released on 2016-04-21 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Trends in Harmonic Analysis and Its Applications

Author : Jens G. Christensen
Publisher :
ISBN 13 : 9781470427771
Total Pages : 218 pages
Book Rating : 4.4/5 (277 download)

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Book Synopsis Trends in Harmonic Analysis and Its Applications by : Jens G. Christensen

Download or read book Trends in Harmonic Analysis and Its Applications written by Jens G. Christensen and published by . This book was released on 2012 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the AMS Special Session on Harmonic Analysis and Its Applications, held March 29-30, 2014, at the University of Maryland, Baltimore County, Baltimore, MD. It provides an in depth look at the many directions taken by experts in Harmonic Analysis and related areas. The papers cover topics such as frame theory, Gabor analysis, interpolation and Besov spaces on compact manifolds, Cuntz-Krieger algebras, reproducing kernel spaces, solenoids, hypergeometric shift operators and analysis on infinite dimensional groups. Expositions are by leading researchers in the field, both young and established. The papers consist of new results or new approaches to solutions, and at the same time provide an introduction into the respective subjects

Harmonic and Complex Analysis and its Applications

Author : Alexander Vasil'ev
Publisher : Springer Science & Business Media
ISBN 13 : 331901806X
Total Pages : 364 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Harmonic and Complex Analysis and its Applications by : Alexander Vasil'ev

Download or read book Harmonic and Complex Analysis and its Applications written by Alexander Vasil'ev and published by Springer Science & Business Media. This book was released on 2013-11-09 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume highlights the main results of the research performed within the network “Harmonic and Complex Analysis and its Applications” (HCAA), which was a five-year (2007–2012) European Science Foundation Programme intended to explore and to strengthen the bridge between two scientific communities: analysts with broad backgrounds in complex and harmonic analysis and mathematical physics, and specialists in physics and applied sciences. It coordinated actions for advancing harmonic and complex analysis and for expanding its application to challenging scientific problems. Particular topics considered by this Programme included conformal and quasiconformal mappings, potential theory, Banach spaces of analytic functions and their applications to the problems of fluid mechanics, conformal field theory, Hamiltonian and Lagrangian mechanics, and signal processing. This book is a collection of surveys written as a result of activities of the Programme and will be interesting and useful for professionals and novices in analysis and mathematical physics, as well as for graduate students. Browsing the volume, the reader will undoubtedly notice that, as the scope of the Programme is rather broad, there are many interrelations between the various contributions, which can be regarded as different facets of a common theme.

Recent Applications of Harmonic Analysis to Function Spaces, Differential Equations, and Data Science

Author : Isaac Pesenson
Publisher : Birkhäuser
ISBN 13 : 3319555561
Total Pages : 512 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Recent Applications of Harmonic Analysis to Function Spaces, Differential Equations, and Data Science by : Isaac Pesenson

Download or read book Recent Applications of Harmonic Analysis to Function Spaces, Differential Equations, and Data Science written by Isaac Pesenson and published by Birkhäuser. This book was released on 2017-08-09 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second of a two volume set on novel methods in harmonic analysis, this book draws on a number of original research and survey papers from well-known specialists detailing the latest innovations and recently discovered links between various fields. Along with many deep theoretical results, these volumes contain numerous applications to problems in signal processing, medical imaging, geodesy, statistics, and data science. The chapters within cover an impressive range of ideas from both traditional and modern harmonic analysis, such as: the Fourier transform, Shannon sampling, frames, wavelets, functions on Euclidean spaces, analysis on function spaces of Riemannian and sub-Riemannian manifolds, Fourier analysis on manifolds and Lie groups, analysis on combinatorial graphs, sheaves, co-sheaves, and persistent homologies on topological spaces. Volume II is organized around the theme of recent applications of harmonic analysis to function spaces, differential equations, and data science, covering topics such as: The classical Fourier transform, the non-linear Fourier transform (FBI transform), cardinal sampling series and translation invariant linear systems. Recent results concerning harmonic analysis on non-Euclidean spaces such as graphs and partially ordered sets. Applications of harmonic analysis to data science and statistics Boundary-value problems for PDE's including the Runge–Walsh theorem for the oblique derivative problem of physical geodesy.

Advances in Gabor Analysis

Author : Hans G. Feichtinger
Publisher : Springer Science & Business Media
ISBN 13 : 1461201330
Total Pages : 369 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Advances in Gabor Analysis by : Hans G. Feichtinger

Download or read book Advances in Gabor Analysis written by Hans G. Feichtinger and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Applied and Numerical Harmonic Analysis (ANHA) book series aims to provide the engineering, mathematical, and scientific communities with significant developments in harmonic analysis, ranging from abstract har monic analysis to basic applications. The title of the series reflects the im portance 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 interleaving of theory and applications and their creative symbi otic evolution is axiomatic. Harmonic analysis is a wellspring of ideas and applicability that has flour ished, developed, and deepened over time within many disciplines and by means of creative cross-fertilization with diverse areas. The intricate and fundamental relationship between harmonic analysis and fields such as sig nal processing, partial differential equations (PDEs), and image processing is reflected 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.

Harmonic Analysis and Applications

Author : Christopher Heil
Publisher : Springer Science & Business Media
ISBN 13 : 0817645047
Total Pages : 390 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Harmonic Analysis and Applications by : Christopher Heil

Download or read book Harmonic Analysis and Applications written by Christopher Heil and published by Springer Science & Business Media. This book was released on 2007-08-02 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Four Short Courses on Harmonic Analysis

Author : Brigitte Forster
Publisher : Springer Science & Business Media
ISBN 13 : 0817648909
Total Pages : 265 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Four Short Courses on Harmonic Analysis by : Brigitte Forster

Download or read book Four Short Courses on Harmonic Analysis written by Brigitte Forster and published by Springer Science & Business Media. This book was released on 2010 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by internationally renowned mathematicians, this state-of-the-art textbook examines four research directions in harmonic analysis and features some of the latest applications in the field. The work is the first one that combines spline theory, wavelets, frames, and time-frequency methods leading up to a construction of wavelets on manifolds other than Rn. Four Short Courses on Harmonic Analysis is intended as a graduate-level textbook for courses or seminars on harmonic analysis and its applications. The work is also an excellent reference or self-study guide for researchers and practitioners with diverse mathematical backgrounds working in different fields such as pure and applied mathematics, image and signal processing engineering, mathematical physics, and communication theory.

Recent Advances in Harmonic Analysis and Applications

Author : Dmitriy Bilyk
Publisher : Springer Science & Business Media
ISBN 13 : 1461445647
Total Pages : 400 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Recent Advances in Harmonic Analysis and Applications by : Dmitriy Bilyk

Download or read book Recent Advances in Harmonic Analysis and Applications written by Dmitriy Bilyk and published by Springer Science & Business Media. This book was released on 2012-10-16 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent Advances in Harmonic Analysis and Applications features selected contributions from the AMS conference which took place at Georgia Southern University, Statesboro in 2011 in honor of Professor Konstantin Oskolkov's 65th birthday. The contributions are based on two special sessions, namely "Harmonic Analysis and Applications" and "Sparse Data Representations and Applications." Topics covered range from Banach space geometry to classical harmonic analysis and partial differential equations. Survey and expository articles by leading experts in their corresponding fields are included, and the volume also features selected high quality papers exploring new results and trends in Muckenhoupt-Sawyer theory, orthogonal polynomials, trigonometric series, approximation theory, Bellman functions and applications in differential equations. Graduate students and researchers in analysis will be particularly interested in the articles which emphasize remarkable connections between analysis and analytic number theory. The readers will learn about recent mathematical developments and directions for future work in the unexpected and surprising interaction between abstract problems in additive number theory and experimentally discovered optical phenomena in physics. This book will be useful for number theorists, harmonic analysts, algorithmists in multi-dimensional signal processing and experts in physics and partial differential equations.