Fourier Analysis On Finite Abelian Groups PDF Download
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Author | : Bao Luong |
Publisher | : Springer Science & Business Media |
Total Pages | : 167 |
Release | : 2009-08-14 |
Genre | : Mathematics |
ISBN | : 0817649166 |
Download Fourier Analysis on Finite Abelian Groups Book in PDF, ePub and Kindle
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 | : Audrey Terras |
Publisher | : Cambridge University Press |
Total Pages | : 456 |
Release | : 1999-03-28 |
Genre | : Mathematics |
ISBN | : 9780521457187 |
Download Fourier Analysis on Finite Groups and Applications Book in PDF, ePub and Kindle
It examines the theory of finite groups in a manner that is both accessible to the beginner and suitable for graduate research.
Author | : Radomir S. Stankovic |
Publisher | : John Wiley & Sons |
Total Pages | : 230 |
Release | : 2005-08-08 |
Genre | : Science |
ISBN | : 0471745421 |
Download Fourier Analysis on Finite Groups with Applications in Signal Processing and System Design Book in PDF, ePub and Kindle
Discover applications of Fourier analysis on finite non-Abeliangroups The majority of publications in spectral techniques considerFourier transform on Abelian groups. However, non-Abelian groupsprovide notable advantages in efficient implementations of spectralmethods. Fourier Analysis on Finite Groups with Applications in SignalProcessing and System Design examines aspects of Fourieranalysis on finite non-Abelian groups and discusses differentmethods used to determine compact representations for discretefunctions providing for their efficient realizations and relatedapplications. Switching functions are included as an example ofdiscrete functions in engineering practice. Additionally,consideration is given to the polynomial expressions and decisiondiagrams defined in terms of Fourier transform on finitenon-Abelian groups. A solid foundation of this complex topic is provided bybeginning with a review of signals and their mathematical modelsand Fourier analysis. Next, the book examines recent achievementsand discoveries in: Matrix interpretation of the fast Fourier transform Optimization of decision diagrams Functional expressions on quaternion groups Gibbs derivatives on finite groups Linear systems on finite non-Abelian groups Hilbert transform on finite groups Among the highlights is an in-depth coverage of applications ofabstract harmonic analysis on finite non-Abelian groups in compactrepresentations of discrete functions and related tasks in signalprocessing and system design, including logic design. All chaptersare self-contained, each with a list of references to facilitatethe development of specialized courses or self-study. With nearly 100 illustrative figures and fifty tables, this isan excellent textbook for graduate-level students and researchersin signal processing, logic design, and system theory-as well asthe more general topics of computer science and appliedmathematics.
Author | : Elias M. Stein |
Publisher | : Princeton University Press |
Total Pages | : 326 |
Release | : 2011-02-11 |
Genre | : Mathematics |
ISBN | : 1400831237 |
Download Fourier Analysis Book in PDF, ePub and Kindle
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 | : Loren N. Argabright |
Publisher | : American Mathematical Soc. |
Total Pages | : 61 |
Release | : 1974 |
Genre | : Abelian groups |
ISBN | : 0821818457 |
Download Fourier Analysis of Unbounded Measures on Locally Compact Abelian Groups Book in PDF, ePub and Kindle
In harmonic analysis on a LCA group G, the term "Fourier transform" has a variety of meanings. It refers to various objects constructed in special ways, depending on the desired theory. The standard theories include the theory of Fourier-Stieltjes transforms, the Plancherel theorem, and the Bochner theorem can be viewed as another aspect of this phenomenon. However, except for special cases, we know of no attempt in the literature to undertake the desired synthesis. The purpose of the present work is to give a systematic account of such an attempt.
Author | : Walter Rudin |
Publisher | : Courier Dover Publications |
Total Pages | : 305 |
Release | : 2017-04-19 |
Genre | : Mathematics |
ISBN | : 0486821013 |
Download Fourier Analysis on Groups Book in PDF, ePub and Kindle
Self-contained treatment by a master mathematical expositor ranges from introductory chapters on basic theorems of Fourier analysis and structure of locally compact Abelian groups to extensive appendixes on topology, topological groups, more. 1962 edition.
Author | : Dinakar Ramakrishnan |
Publisher | : Springer Science & Business Media |
Total Pages | : 372 |
Release | : 2013-04-17 |
Genre | : Mathematics |
ISBN | : 1475730853 |
Download Fourier Analysis on Number Fields Book in PDF, ePub and Kindle
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 | : Benjamin Steinberg |
Publisher | : Springer Science & Business Media |
Total Pages | : 166 |
Release | : 2011-10-23 |
Genre | : Mathematics |
ISBN | : 1461407761 |
Download Representation Theory of Finite Groups Book in PDF, ePub and Kindle
This book is intended to present group representation theory at a level accessible to mature undergraduate students and beginning graduate students. This is achieved by mainly keeping the required background to the level of undergraduate linear algebra, group theory and very basic ring theory. Module theory and Wedderburn theory, as well as tensor products, are deliberately avoided. Instead, we take an approach based on discrete Fourier Analysis. Applications to the spectral theory of graphs are given to help the student appreciate the usefulness of the subject. A number of exercises are included. This book is intended for a 3rd/4th undergraduate course or an introductory graduate course on group representation theory. However, it can also be used as a reference for workers in all areas of mathematics and statistics.
Author | : Tullio Ceccherini-Silberstein |
Publisher | : Cambridge University Press |
Total Pages | : 589 |
Release | : 2018-06-21 |
Genre | : Mathematics |
ISBN | : 1107182336 |
Download Discrete Harmonic Analysis Book in PDF, ePub and Kindle
A self-contained introduction to discrete harmonic analysis with an emphasis on the Discrete and Fast Fourier Transforms.
Author | : Hans G. Feichtinger |
Publisher | : Springer Science & Business Media |
Total Pages | : 507 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461220165 |
Download Gabor Analysis and Algorithms Book in PDF, ePub and Kindle
In his paper Theory of Communication [Gab46], D. Gabor proposed the use of a family of functions obtained from one Gaussian by time-and frequency shifts. Each of these is well concentrated in time and frequency; together they are meant to constitute a complete collection of building blocks into which more complicated time-depending functions can be decomposed. The application to communication proposed by Gabor was to send the coeffi cients of the decomposition into this family of a signal, rather than the signal itself. This remained a proposal-as far as I know there were no seri ous attempts to implement it for communication purposes in practice, and in fact, at the critical time-frequency density proposed originally, there is a mathematical obstruction; as was understood later, the family of shifted and modulated Gaussians spans the space of square integrable functions [BBGK71, Per71] (it even has one function to spare [BGZ75] . . . ) but it does not constitute what we now call a frame, leading to numerical insta bilities. The Balian-Low theorem (about which the reader can find more in some of the contributions in this book) and its extensions showed that a similar mishap occurs if the Gaussian is replaced by any other function that is "reasonably" smooth and localized. One is thus led naturally to considering a higher time-frequency density.