Factoring Groups into Subsets

Author: Sandor Szabo,Arthur D. Sands
Publisher: CRC Press
ISBN: 9781420090475
Category: Mathematics
Page: 274
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Decomposing an abelian group into a direct sum of its subsets leads to results that can be applied to a variety of areas, such as number theory, geometry of tilings, coding theory, cryptography, graph theory, and Fourier analysis. Focusing mainly on cyclic groups, Factoring Groups into Subsets explores the factorization theory of abelian groups. The book first shows how to construct new factorizations from old ones. The authors then discuss nonperiodic and periodic factorizations, quasiperiodicity, and the factoring of periodic subsets. They also examine how tiling plays an important role in number theory. The next several chapters cover factorizations of infinite abelian groups; combinatorics, such as Ramsey numbers, Latin squares, and complex Hadamard matrices; and connections with codes, including variable length codes, error correcting codes, and integer codes. The final chapter deals with several classical problems of Fuchs. Encompassing many of the main areas of the factorization theory, this book explores problems in which the underlying factored group is cyclic.

Trends in Harmonic Analysis

Author: Massimo A. Picardello
Publisher: Springer Science & Business Media
ISBN: 8847028531
Category: Mathematics
Page: 448
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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).

Random Walks and Discrete Potential Theory

Author: M. Picardello,W. Woess
Publisher: Cambridge University Press
ISBN: 9780521773126
Category: Mathematics
Page: 361
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Comprehensive and interdisciplinary text covering the interplay between random walks and structure theory.

Analytic, Algebraic and Geometric Aspects of Differential Equations

Będlewo, Poland, September 2015
Author: Galina Filipuk,Yoshishige Haraoka,Sławomir Michalik
Publisher: Birkhäuser
ISBN: 3319528424
Category: Mathematics
Page: 471
View: 1076

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This volume consists of invited lecture notes, survey papers and original research papers from the AAGADE school and conference held in Będlewo, Poland in September 2015. The contributions provide an overview of the current level of interaction between algebra, geometry and analysis and demonstrate the manifold aspects of the theory of ordinary and partial differential equations, while also pointing out the highly fruitful interrelations between those aspects. These interactions continue to yield new developments, not only in the theory of differential equations but also in several related areas of mathematics and physics such as differential geometry, representation theory, number theory and mathematical physics. The main goal of the volume is to introduce basic concepts, techniques, detailed and illustrative examples and theorems (in a manner suitable for non-specialists), and to present recent developments in the field, together with open problems for more advanced and experienced readers. It will be of interest to graduate students, early-career researchers and specialists in analysis, geometry, algebra and related areas, as well as anyone interested in learning new methods and techniques.

Operator Algebras and Operator Theory

International Conference on Operator Algebras and Operator Theory, July 4-9, 1997, Shanghai, China
Author: Liming Ge
Publisher: American Mathematical Soc.
ISBN: 0821810936
Category: Mathematics
Page: 389
View: 9683

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This volume contains the proceedings from the International Conference on Operator Algebras and Operator Theory held at the East China Normal University in Shanghai (China). Participants in the conference ranged from graduate students to postdocs to leading experts who came from around the world. Topics covered in this title were $C^*$-algebras, von Neumann algebras, non-self-adjoint operator algebras, wavelets, operator spaces and other related areas. This work consists of contributions from invited speakers and some mathematicians who were unable to attend. It presents important mathematical ideas while maintaining the uniqueness and excitement of this very successful event.

Modern Theory of Dynamical Systems: A Tribute to Dmitry Victorovich Anosov

Author: Anatole Katok,Yakov Pesin,Federico Rodriguez Hertz
Publisher: American Mathematical Soc.
ISBN: 1470425602
Category: Boundary value problems
Page: 320
View: 2879

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This volume is a tribute to one of the founders of modern theory of dynamical systems, the late Dmitry Victorovich Anosov. It contains both original papers and surveys, written by some distinguished experts in dynamics, which are related to important themes of Anosov's work, as well as broadly interpreted further crucial developments in the theory of dynamical systems that followed Anosov's original work. Also included is an article by A. Katok that presents Anosov's scientific biography and a picture of the early development of hyperbolicity theory in its various incarnations, complete and partial, uniform and nonuniform.

Fourier Analysis on Finite Groups and Applications

Author: Audrey Terras
Publisher: Cambridge University Press
ISBN: 9780521457187
Category: Mathematics
Page: 442
View: 4840

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A friendly introduction to Fourier analysis on finite groups, accessible to undergraduates/graduates in mathematics, engineering and the physical sciences.

Fourier Analysis on Finite Abelian Groups

Author: Bao Luong
Publisher: Springer Science & Business Media
ISBN: 0817649166
Category: Mathematics
Page: 159
View: 2025

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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.

Harmonic Analysis on Spaces of Homogeneous Type

Author: Donggao Deng,Yongsheng Han
Publisher: Springer Science & Business Media
ISBN: 354088744X
Category: Mathematics
Page: 160
View: 1375

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This book could have been entitled “Analysis and Geometry.” The authors are addressing the following issue: Is it possible to perform some harmonic analysis on a set? Harmonic analysis on groups has a long tradition. Here we are given a metric set X with a (positive) Borel measure ? and we would like to construct some algorithms which in the classical setting rely on the Fourier transformation. Needless to say, the Fourier transformation does not exist on an arbitrary metric set. This endeavor is not a revolution. It is a continuation of a line of research whichwasinitiated,acenturyago,withtwofundamentalpapersthatIwould like to discuss brie?y. The ?rst paper is the doctoral dissertation of Alfred Haar, which was submitted at to University of Gottingen ̈ in July 1907. At that time it was known that the Fourier series expansion of a continuous function may diverge at a given point. Haar wanted to know if this phenomenon happens for every 2 orthonormal basis of L [0,1]. He answered this question by constructing an orthonormal basis (today known as the Haar basis) with the property that the expansion (in this basis) of any continuous function uniformly converges to that function.

Continuum Theory

An Introduction
Author: Sam Nadler
Publisher: CRC Press
ISBN: 1351990535
Category: Mathematics
Page: 348
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A textbook for either a semester or year course for graduate students of mathematics who have had at least one course in topology. Introduces continuum theory through a combination of classical and modern techniques. Annotation copyright Book News, Inc. Portland, Or.

Symposia mathematica

Author: Istituto nazionale di alta matematica (Italy),Istituto nazionale di alta matematica Francesco Severi
Publisher: N.A
Category: Mathematics
Page: N.A
View: 4876

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Fourier Analysis on Groups

Author: Walter Rudin
Publisher: Courier Dover Publications
ISBN: 0486821013
Category: Mathematics
Page: 304
View: 4136

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Written by a master mathematical expositor, this classic text reflects the results of the intense period of research and development in the area of Fourier analysis in the decade preceding its first publication in 1962. The enduringly relevant treatment is geared toward advanced undergraduate and graduate students and has served as a fundamental resource for more than five decades. The self-contained text opens with an overview of the basic theorems of Fourier analysis and the structure of locally compact Abelian groups. Subsequent chapters explore idempotent measures, homomorphisms of group algebras, measures and Fourier transforms on thin sets, functions of Fourier transforms, closed ideals in L1(G), Fourier analysis on ordered groups, and closed subalgebras of L1(G). Helpful Appendixes contain background information on topology and topological groups, Banach spaces and algebras, and measure theory.

Fourier Analysis on Number Fields

Author: Dinakar Ramakrishnan,Robert J. Valenza
Publisher: Springer Science & Business Media
ISBN: 1475730853
Category: Mathematics
Page: 354
View: 1791

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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.