Fourier Analysis On Number Fields

Author : Dinakar Ramakrishnan,Robert J. Valenza
Publisher : Springer Science & Business Media
Page : 372 pages
File Size : 51,6 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781475730852

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Fourier Analysis on Number Fields by Dinakar Ramakrishnan,Robert J. Valenza Pdf

A modern approach to number theory through a blending of complementary algebraic and analytic perspectives, emphasising harmonic analysis on topological groups. The main goal is to cover John Tates visionary thesis, giving virtually all of the necessary analytic details and topological preliminaries -- technical prerequisites that are often foreign to the typical, more algebraically inclined number theorist. While most of the existing treatments of Tates thesis are somewhat terse and less than complete, the intent here is to be more leisurely, more comprehensive, and more comprehensible. While the choice of objects and methods is naturally guided by specific mathematical goals, the approach is by no means narrow. In fact, the subject matter at hand is germane not only to budding number theorists, but also to students of harmonic analysis or the representation theory of Lie groups. The text addresses students who have taken a year of graduate-level course in algebra, analysis, and topology. Moreover, the work will act as a good reference for working mathematicians interested in any of these fields.

Author : M. H. Taibleson
Publisher : Princeton University Press
Page : 308 pages
File Size : 53,8 Mb
Release : 2015-03-08
Category : Mathematics
ISBN : 9781400871339

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Fourier Analysis on Local Fields. (MN-15) by M. H. Taibleson Pdf

This book presents a development of the basic facts about harmonic analysis on local fields and the n-dimensional vector spaces over these fields. It focuses almost exclusively on the analogy between the local field and Euclidean cases, with respect to the form of statements, the manner of proof, and the variety of applications. The force of the analogy between the local field and Euclidean cases rests in the relationship of the field structures that underlie the respective cases. A complete classification of locally compact, non-discrete fields gives us two examples of connected fields (real and complex numbers); the rest are local fields (p-adic numbers, p-series fields, and their algebraic extensions). The local fields are studied in an effort to extend knowledge of the reals and complexes as locally compact fields. The author's central aim has been to present the basic facts of Fourier analysis on local fields in an accessible form and in the same spirit as in Zygmund's Trigonometric Series (Cambridge, 1968) and in Introduction to Fourier Analysis on Euclidean Spaces by Stein and Weiss (1971). Originally published in 1975. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Author : Bao Luong
Publisher : Springer Science & Business Media
Page : 167 pages
File Size : 55,6 Mb
Release : 2009-08-14
Category : Mathematics
ISBN : 9780817649166

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Fourier Analysis on Finite Abelian Groups by Bao Luong Pdf

This unified, self-contained book examines the mathematical tools used for decomposing and analyzing functions, specifically, the application of the [discrete] Fourier transform to finite Abelian groups. With countless examples and unique exercise sets at the end of each section, Fourier Analysis on Finite Abelian Groups is a perfect companion to a first course in Fourier analysis. This text introduces mathematics students to subjects that are within their reach, but it also has powerful applications that may appeal to advanced researchers and mathematicians. The only prerequisites necessary are group theory, linear algebra, and complex analysis.

Author : Russell L. Herman
Publisher : CRC Press
Page : 527 pages
File Size : 43,9 Mb
Release : 2016-09-19
Category : Mathematics
ISBN : 9781498773720

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An Introduction to Fourier Analysis by Russell L. Herman Pdf

This book helps students explore Fourier analysis and its related topics, helping them appreciate why it pervades many fields of mathematics, science, and engineering. This introductory textbook was written with mathematics, science, and engineering students with a background in calculus and basic linear algebra in mind. It can be used as a textbook for undergraduate courses in Fourier analysis or applied mathematics, which cover Fourier series, orthogonal functions, Fourier and Laplace transforms, and an introduction to complex variables. These topics are tied together by the application of the spectral analysis of analog and discrete signals, and provide an introduction to the discrete Fourier transform. A number of examples and exercises are provided including implementations of Maple, MATLAB, and Python for computing series expansions and transforms. After reading this book, students will be familiar with: • Convergence and summation of infinite series • Representation of functions by infinite series • Trigonometric and Generalized Fourier series • Legendre, Bessel, gamma, and delta functions • Complex numbers and functions • Analytic functions and integration in the complex plane • Fourier and Laplace transforms. • The relationship between analog and digital signals Dr. Russell L. Herman is a professor of Mathematics and Professor of Physics at the University of North Carolina Wilmington. A recipient of several teaching awards, he has taught introductory through graduate courses in several areas including applied mathematics, partial differential equations, mathematical physics, quantum theory, optics, cosmology, and general relativity. His research interests include topics in nonlinear wave equations, soliton perturbation theory, fluid dynamics, relativity, chaos and dynamical systems.

Author : Tullio Ceccherini-Silberstein,Fabio Scarabotti,Filippo Tolli
Publisher : Cambridge University Press
Page : 589 pages
File Size : 49,6 Mb
Release : 2018-06-21
Category : Mathematics
ISBN : 9781107182332

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Discrete Harmonic Analysis by Tullio Ceccherini-Silberstein,Fabio Scarabotti,Filippo Tolli Pdf

A self-contained introduction to discrete harmonic analysis with an emphasis on the Discrete and Fast Fourier Transforms.

Author : Luca Brandolini,Leonardo Colzani,Alex Iosevich,Giancarlo Travaglini
Publisher : Springer Science & Business Media
Page : 268 pages
File Size : 43,5 Mb
Release : 2011-04-27
Category : Mathematics
ISBN : 9780817681722

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Fourier Analysis and Convexity by Luca Brandolini,Leonardo Colzani,Alex Iosevich,Giancarlo Travaglini Pdf

Explores relationship between Fourier Analysis, convex geometry, and related areas; in the past, study of this relationship has led to important mathematical advances Presents new results and applications to diverse fields such as geometry, number theory, and analysis Contributors are leading experts in their respective fields Will be of interest to both pure and applied mathematicians

Author : Elias M. Stein,Rami Shakarchi
Publisher : Princeton University Press
Page : 326 pages
File Size : 54,5 Mb
Release : 2011-02-11
Category : Mathematics
ISBN : 9781400831234

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Fourier Analysis by Elias M. Stein,Rami Shakarchi Pdf

This first volume, a three-part introduction to the subject, is intended for students with a beginning knowledge of mathematical analysis who are motivated to discover the ideas that shape Fourier analysis. It begins with the simple conviction that Fourier arrived at in the early nineteenth century when studying problems in the physical sciences--that an arbitrary function can be written as an infinite sum of the most basic trigonometric functions. The first part implements this idea in terms of notions of convergence and summability of Fourier series, while highlighting applications such as the isoperimetric inequality and equidistribution. The second part deals with the Fourier transform and its applications to classical partial differential equations and the Radon transform; a clear introduction to the subject serves to avoid technical difficulties. The book closes with Fourier theory for finite abelian groups, which is applied to prime numbers in arithmetic progression. In organizing their exposition, the authors have carefully balanced an emphasis on key conceptual insights against the need to provide the technical underpinnings of rigorous analysis. Students of mathematics, physics, engineering and other sciences will find the theory and applications covered in this volume to be of real interest. The Princeton Lectures in Analysis represents a sustained effort to introduce the core areas of mathematical analysis while also illustrating the organic unity between them. Numerous examples and applications throughout its four planned volumes, of which Fourier Analysis is the first, highlight the far-reaching consequences of certain ideas in analysis to other fields of mathematics and a variety of sciences. Stein and Shakarchi move from an introduction addressing Fourier series and integrals to in-depth considerations of complex analysis; measure and integration theory, and Hilbert spaces; and, finally, further topics such as functional analysis, distributions and elements of probability theory.

Author : Andre Weil
Publisher : Springer Science & Business Media
Page : 335 pages
File Size : 40,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642619458

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Basic Number Theory by Andre Weil Pdf

From the reviews: "L.R. Shafarevich showed me the first edition [...] and said that this book will be from now on the book about class field theory. In fact it is by far the most complete treatment of the main theorems of algebraic number theory, including function fields over finite constant fields, that appeared in book form." Zentralblatt MATH

Author : Tim Olson
Publisher : Birkhäuser
Page : 302 pages
File Size : 46,6 Mb
Release : 2017-11-20
Category : Mathematics
ISBN : 9781493973934

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Applied Fourier Analysis by Tim Olson Pdf

The first of its kind, this focused textbook serves as a self-contained resource for teaching from scratch the fundamental mathematics of Fourier analysis and illustrating some of its most current, interesting applications, including medical imaging and radar processing. Developed by the author from extensive classroom teaching experience, it provides a breadth of theory that allows students to appreciate the utility of the subject, but at as accessible a depth as possible. With myriad applications included, this book can be adapted to a one or two semester course in Fourier Analysis or serve as the basis for independent study. Applied Fourier Analysis assumes no prior knowledge of analysis from its readers, and begins by making the transition from linear algebra to functional analysis. It goes on to cover basic Fourier series and Fourier transforms before delving into applications in sampling and interpolation theory, digital communications, radar processing, medi cal imaging, and heat and wave equations. For all applications, ample practice exercises are given throughout, with collections of more in-depth problems built up into exploratory chapter projects. Illuminating videos are available on Springer.com and Link.Springer.com that present animated visualizations of several concepts. The content of the book itself is limited to what students will need to deal with in these fields, and avoids spending undue time studying proofs or building toward more abstract concepts. The book is perhaps best suited for courses aimed at upper division undergraduates and early graduates in mathematics, electrical engineering, mechanical engineering, computer science, physics, and other natural sciences, but in general it is a highly valuable resource for introducing a broad range of students to Fourier analysis.

Author : Vasili? Sergeevich Vladimirov,I. V. Volovich,E. I. Zelenov
Publisher : World Scientific
Page : 350 pages
File Size : 51,8 Mb
Release : 1994
Category : Science
ISBN : 9810208804

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P-adic Analysis and Mathematical Physics by Vasili? Sergeevich Vladimirov,I. V. Volovich,E. I. Zelenov Pdf

p-adic numbers play a very important role in modern number theory, algebraic geometry and representation theory. Lately p-adic numbers have attracted a great deal of attention in modern theoretical physics as a promising new approach for describing the non-Archimedean geometry of space-time at small distances.This is the first book to deal with applications of p-adic numbers in theoretical and mathematical physics. It gives an elementary and thoroughly written introduction to p-adic numbers and p-adic analysis with great numbers of examples as well as applications of p-adic numbers in classical mechanics, dynamical systems, quantum mechanics, statistical physics, quantum field theory and string theory.

Author : Hershel M. Farkas,Robert C. Gunning,Marvin I. Knopp,B. A. Taylor
Publisher : Springer Science & Business Media
Page : 563 pages
File Size : 45,8 Mb
Release : 2012-09-18
Category : Mathematics
ISBN : 9781461440758

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From Fourier Analysis and Number Theory to Radon Transforms and Geometry by Hershel M. Farkas,Robert C. Gunning,Marvin I. Knopp,B. A. Taylor Pdf

​​​A memorial conference for Leon Ehrenpreis was held at Temple University, November 15-16, 2010. In the spirit of Ehrenpreis’s contribution to mathematics, the papers in this volume, written by prominent mathematicians, represent the wide breadth of subjects that Ehrenpreis traversed in his career, including partial differential equations, combinatorics, number theory, complex analysis and a bit of applied mathematics. With the exception of one survey article, the papers in this volume are all new results in the various fields in which Ehrenpreis worked . There are papers in pure analysis, papers in number theory, papers in what may be called applied mathematics such as population biology and parallel refractors and papers in partial differential equations. The mature mathematician will find new mathematics and the advanced graduate student will find many new ideas to explore.​A biographical sketch of Leon Ehrenpreis by his daughter, a professional journalist, enhances the memorial tribute and gives the reader a glimpse into the life and career of a great mathematician.

Author : M. H. Taibleson
Publisher : Unknown
Page : 307 pages
File Size : 47,8 Mb
Release : 1975-01-01
Category : Electronic
ISBN : 0608066419

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Fourier Analysis on Local Fields by M. H. Taibleson Pdf

Author : Sinai Robins
Publisher : American Mathematical Society
Page : 352 pages
File Size : 40,9 Mb
Release : 2024-04-24
Category : Mathematics
ISBN : 9781470470333

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Fourier Analysis on Polytopes and the Geometry of Numbers by Sinai Robins Pdf

This book offers a gentle introduction to the geometry of numbers from a modern Fourier-analytic point of view. One of the main themes is the transfer of geometric knowledge of a polytope to analytic knowledge of its Fourier transform. The Fourier transform preserves all of the information of a polytope, and turns its geometry into analysis. The approach is unique, and streamlines this emerging field by presenting new simple proofs of some basic results of the field. In addition, each chapter is fitted with many exercises, some of which have solutions and hints in an appendix. Thus, an individual learner will have an easier time absorbing the material on their own, or as part of a class. Overall, this book provides an introduction appropriate for an advanced undergraduate, a beginning graduate student, or researcher interested in exploring this important expanding field.

Author : Ryan O'Donnell
Publisher : Cambridge University Press
Page : 445 pages
File Size : 50,9 Mb
Release : 2014-06-05
Category : Computers
ISBN : 9781107038325

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Analysis of Boolean Functions by Ryan O'Donnell Pdf

This graduate-level text gives a thorough overview of the analysis of Boolean functions, beginning with the most basic definitions and proceeding to advanced topics.

Author : R. Vichnevetsky,J. B. Bowles
Publisher : SIAM
Page : 146 pages
File Size : 43,5 Mb
Release : 1982-01-01
Category : Technology & Engineering
ISBN : 9780898713923

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Fourier Analysis of Numerical Approximations of Hyperbolic Equations by R. Vichnevetsky,J. B. Bowles Pdf

This book provides useful reference material for those concerned with the use of Fourier analysis and computational fluid dynamics.