Harmonic Analysis And Applications

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Harmonic Analysis and Applications

Carlos E. Kenig
Harmonic Analysis and Applications Book PDF

Author : Carlos E. Kenig
Publisher : American Mathematical Soc.
Page : 345 pages
File Size : 50,8 Mb
Release : 2020-12-14
Category : Education
ISBN : 9781470461270

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Harmonic Analysis and Applications by Carlos E. Kenig Pdf

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.

Harmonic Analysis and Applications

John J. Benedetto
Harmonic Analysis and Applications Book PDF

Author : John J. Benedetto
Publisher : CRC Press
Page : 370 pages
File Size : 53,8 Mb
Release : 1996-07-29
Category : Mathematics
ISBN : 0849378796

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Harmonic Analysis and Applications by John J. Benedetto Pdf

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 Advances in Harmonic Analysis and Applications

Dmitriy Bilyk,Laura De Carli,Alexander Petukhov,Alexander M. Stokolos,Brett D. Wick
Recent Advances in Harmonic Analysis and Applications Book PDF

Author : Dmitriy Bilyk,Laura De Carli,Alexander Petukhov,Alexander M. Stokolos,Brett D. Wick
Publisher : Springer Science & Business Media
Page : 400 pages
File Size : 46,5 Mb
Release : 2012-10-16
Category : Mathematics
ISBN : 9781461445647

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Recent Advances in Harmonic Analysis and Applications by Dmitriy Bilyk,Laura De Carli,Alexander Petukhov,Alexander M. Stokolos,Brett D. Wick Pdf

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.

Non-Abelian Harmonic Analysis

Roger E. Howe,Eng Chye Tan
Non Abelian Harmonic Analysis Book PDF

Author : Roger E. Howe,Eng Chye Tan
Publisher : Springer Science & Business Media
Page : 271 pages
File Size : 40,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461392002

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Non-Abelian Harmonic Analysis by Roger E. Howe,Eng Chye Tan Pdf

This book mainly discusses the representation theory of the special linear group 8L(2, 1R), and some applications of this theory. In fact the emphasis is on the applications; the working title of the book while it was being writ ten was "Some Things You Can Do with 8L(2). " Some of the applications are outside representation theory, and some are to representation theory it self. The topics outside representation theory are mostly ones of substantial classical importance (Fourier analysis, Laplace equation, Huyghens' prin ciple, Ergodic theory), while the ones inside representation theory mostly concern themes that have been central to Harish-Chandra's development of harmonic analysis on semisimple groups (his restriction theorem, regularity theorem, character formulas, and asymptotic decay of matrix coefficients and temperedness). We hope this mix of topics appeals to nonspecialists in representation theory by illustrating (without an interminable prolegom ena) how representation theory can offer new perspectives on familiar topics and by offering some insight into some important themes in representation theory itself. Especially, we hope this book popularizes Harish-Chandra's restriction formula, which, besides being basic to his work, is simply a beautiful example of Fourier analysis on Euclidean space. We also hope representation theorists will enjoy seeing examples of how their subject can be used and will be stimulated by some of the viewpoints offered on representation-theoretic issues.

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 : 48,8 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.

Harmonic Analysis

María Cristina Pereyra,Lesley A. Ward
Harmonic Analysis Book PDF

Author : María Cristina Pereyra,Lesley A. Ward
Publisher : American Mathematical Soc.
Page : 437 pages
File Size : 41,8 Mb
Release : 2012
Category : Mathematics
ISBN : 9780821875667

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Harmonic Analysis by María Cristina Pereyra,Lesley A. Ward Pdf

Conveys the remarkable beauty and applicability of the ideas that have grown from Fourier theory. It presents for an advanced undergraduate and beginning graduate student audience the basics of harmonic analysis, from Fourier's study of the heat equation, and the decomposition of functions into sums of cosines and sines (frequency analysis), to dyadic harmonic analysis, and the decomposition of functions into a Haar basis (time localization).

Excursions in Harmonic Analysis, Volume 6

Matthew Hirn,Shidong Li,Kasso A. Okoudjou,Sandra Saliani,Özgür Yilmaz
Excursions in Harmonic Analysis Volume 6 Book PDF

Author : Matthew Hirn,Shidong Li,Kasso A. Okoudjou,Sandra Saliani,Özgür Yilmaz
Publisher : Springer Nature
Page : 444 pages
File Size : 42,6 Mb
Release : 2021-09-01
Category : Mathematics
ISBN : 9783030696375

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Excursions in Harmonic Analysis, Volume 6 by Matthew Hirn,Shidong Li,Kasso A. Okoudjou,Sandra Saliani,Özgür Yilmaz Pdf

John J. Benedetto has had a profound influence not only on the direction of harmonic analysis and its applications, but also on the entire community of people involved in the field. The chapters in this volume – compiled on the occasion of his 80th birthday – are written by leading researchers in the field and pay tribute to John’s many significant and lasting achievements. Covering a wide range of topics in harmonic analysis and related areas, these chapters are organized into four main parts: harmonic analysis, wavelets and frames, sampling and signal processing, and compressed sensing and optimization. An introductory chapter also provides a brief overview of John’s life and mathematical career. This volume will be an excellent reference for graduate students, researchers, and professionals in pure and applied mathematics, engineering, and physics.

Principles of Harmonic Analysis

Anton Deitmar,Siegfried Echterhoff
Principles of Harmonic Analysis Book PDF

Author : Anton Deitmar,Siegfried Echterhoff
Publisher : Springer
Page : 332 pages
File Size : 54,9 Mb
Release : 2014-06-21
Category : Mathematics
ISBN : 9783319057927

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Principles of Harmonic Analysis by Anton Deitmar,Siegfried Echterhoff Pdf

This book offers a complete and streamlined treatment of the central principles of abelian harmonic analysis: Pontryagin duality, the Plancherel theorem and the Poisson summation formula, as well as their respective generalizations to non-abelian groups, including the Selberg trace formula. The principles are then applied to spectral analysis of Heisenberg manifolds and Riemann surfaces. This new edition contains a new chapter on p-adic and adelic groups, as well as a complementary section on direct and projective limits. Many of the supporting proofs have been revised and refined. The book is an excellent resource for graduate students who wish to learn and understand harmonic analysis and for researchers seeking to apply it.

Framelets and Wavelets

Bin Han
Framelets and Wavelets Book PDF

Author : Bin Han
Publisher : Springer
Page : 750 pages
File Size : 52,9 Mb
Release : 2018-01-04
Category : Mathematics
ISBN : 9783319685304

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Framelets and Wavelets by Bin Han Pdf

Marking a distinct departure from the perspectives of frame theory and discrete transforms, this book provides a comprehensive mathematical and algorithmic introduction to wavelet theory. As such, it can be used as either a textbook or reference guide. As a textbook for graduate mathematics students and beginning researchers, it offers detailed information on the basic theory of framelets and wavelets, complemented by self-contained elementary proofs, illustrative examples/figures, and supplementary exercises. Further, as an advanced reference guide for experienced researchers and practitioners in mathematics, physics, and engineering, the book addresses in detail a wide range of basic and advanced topics (such as multiwavelets/multiframelets in Sobolev spaces and directional framelets) in wavelet theory, together with systematic mathematical analysis, concrete algorithms, and recent developments in and applications of framelets and wavelets. Lastly, the book can also be used to teach on or study selected special topics in approximation theory, Fourier analysis, applied harmonic analysis, functional analysis, and wavelet-based signal/image processing.

Engineering Applications of Noncommutative Harmonic Analysis

Gregory S. Chirikjian,Alexander B. Kyatkin
Engineering Applications of Noncommutative Harmonic Analysis Book PDF

Author : Gregory S. Chirikjian,Alexander B. Kyatkin
Publisher : CRC Press
Page : 698 pages
File Size : 42,5 Mb
Release : 2000-09-28
Category : Computers
ISBN : 9781420041767

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Engineering Applications of Noncommutative Harmonic Analysis by Gregory S. Chirikjian,Alexander B. Kyatkin Pdf

The classical Fourier transform is one of the most widely used mathematical tools in engineering. However, few engineers know that extensions of harmonic analysis to functions on groups holds great potential for solving problems in robotics, image analysis, mechanics, and other areas. For those that may be aware of its potential value, there is sti

Harmonic Analysis, Signal Processing, and Complexity

Irene Sabadini,Daniele C. Struppa,David F. Walnut
Harmonic Analysis Signal Processing and Complexity Book PDF

Author : Irene Sabadini,Daniele C. Struppa,David F. Walnut
Publisher : Springer Science & Business Media
Page : 172 pages
File Size : 55,9 Mb
Release : 2008-12-16
Category : Mathematics
ISBN : 9780817644161

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Harmonic Analysis, Signal Processing, and Complexity by Irene Sabadini,Daniele C. Struppa,David F. Walnut Pdf

* Original articles and survey articles in honor of the sixtieth birthday of Carlos A. Berenstein reflect his diverse research interests from interpolation to residue theory to deconvolution and its applications to issues ranging from optics to the study of blood flow * Contains both theoretical papers in harmonic and complex analysis, as well as more applied work in signal processing * Top-notch contributors in their respective fields

A Course in Abstract Harmonic Analysis

Gerald B. Folland
A Course in Abstract Harmonic Analysis Book PDF

Author : Gerald B. Folland
Publisher : CRC Press
Page : 317 pages
File Size : 53,9 Mb
Release : 2016-02-03
Category : Mathematics
ISBN : 9781498727150

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A Course in Abstract Harmonic Analysis by Gerald B. Folland Pdf

A Course in Abstract Harmonic Analysis is an introduction to that part of analysis on locally compact groups that can be done with minimal assumptions on the nature of the group. As a generalization of classical Fourier analysis, this abstract theory creates a foundation for a great deal of modern analysis, and it contains a number of elegant resul

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

Isaac Pesenson,Quoc Thong Le Gia,Azita Mayeli,Hrushikesh Mhaskar,Ding-Xuan Zhou
Recent Applications of Harmonic Analysis to Function Spaces Differential Equations and Data Science Book PDF

Author : Isaac Pesenson,Quoc Thong Le Gia,Azita Mayeli,Hrushikesh Mhaskar,Ding-Xuan Zhou
Publisher : Birkhäuser
Page : 0 pages
File Size : 53,6 Mb
Release : 2018-08-03
Category : Mathematics
ISBN : 3319856936

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Recent Applications of Harmonic Analysis to Function Spaces, Differential Equations, and Data Science by Isaac Pesenson,Quoc Thong Le Gia,Azita Mayeli,Hrushikesh Mhaskar,Ding-Xuan Zhou Pdf

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.

Harmonic Analysis and Integral Geometry

Massimo Picardello
Harmonic Analysis and Integral Geometry Book PDF

Author : Massimo Picardello
Publisher : CRC Press
Page : 194 pages
File Size : 49,9 Mb
Release : 2000-09-07
Category : Mathematics
ISBN : 1584881836

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Harmonic Analysis and Integral Geometry by Massimo Picardello Pdf

Comprising a selection of expository and research papers, Harmonic Analysis and Integral Geometry grew from presentations offered at the July 1998 Summer University of Safi, Morocco-an annual, advanced research school and congress. This lively and very successful event drew the attendance of many top researchers, who offered both individual lectures and coordinated courses on specific research topics within this fast growing subject. Harmonic Analysis and Integral Geometry presents important recent advances in the fields of Radon transforms, integral geometry, and harmonic analysis on Lie groups and symmetric spaces. Several articles are devoted to the new theory of Radon transforms on trees. With its related presentations addressing recent developments in various aspects of these intriguing areas of study, Harmonic Analysis and Integral Geometry becomes an important addition not only to the Research Notes in Mathematics series, but to the general mathematics literature.

Harmonic Analysis and Applications

John J. Benedetto
Harmonic Analysis and Applications Book PDF

Author : John J. Benedetto
Publisher : CRC Press
Page : 357 pages
File Size : 44,6 Mb
Release : 2020-12-17
Category : Mathematics
ISBN : 9781000099089

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Harmonic Analysis and Applications by John J. Benedetto Pdf

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.