Semigroups in Algebra, Geometry and Analysis

Semigroups in Algebra, Geometry and Analysis PDF Author: Karl H. Hofmann
Publisher: Walter de Gruyter
ISBN: 3110885581
Category : Mathematics
Languages : en
Pages : 385

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Book Description
The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany Katrin Wendland, University of Freiburg, Germany Honorary Editor Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Titles in planning include Yuri A. Bahturin, Identical Relations in Lie Algebras (2019) Yakov G. Berkovich and Z. Janko, Groups of Prime Power Order, Volume 6 (2019) Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019) Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019) Volker Mayer, Mariusz Urbański, and Anna Zdunik, Random and Conformal Dynamical Systems (2021) Ioannis Diamantis, Boštjan Gabrovšek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)

The Analytical and Topological Theory of Semigroups

The Analytical and Topological Theory of Semigroups PDF Author: Karl Heinrich Hofmann
Publisher: de Gruyter
ISBN: 9783110124897
Category : Topological groups
Languages : en
Pages : 0

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Book Description
Presents trends and developments in diverse areas of semigroup theory such as analysis, functional analysis and topology. Main topics include: Lie theory and algebraic geometry for semigroups; structure theory of compact semigroups; functional analysis on semigroups; relations to systems theory and a combinatorial number theory. Particular emphasis is given to applications in probability theory and semigroups of continuous functions. Annotation copyrighted by Book News, Inc., Portland, OR

Harmonic Analysis on Semigroups

Harmonic Analysis on Semigroups PDF Author: C. van den Berg
Publisher: Springer Science & Business Media
ISBN: 146121128X
Category : Mathematics
Languages : en
Pages : 299

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Book Description
The Fourier transform and the Laplace transform of a positive measure share, together with its moment sequence, a positive definiteness property which under certain regularity assumptions is characteristic for such expressions. This is formulated in exact terms in the famous theorems of Bochner, Bernstein-Widder and Hamburger. All three theorems can be viewed as special cases of a general theorem about functions qJ on abelian semigroups with involution (S, +, *) which are positive definite in the sense that the matrix (qJ(sJ + Sk» is positive definite for all finite choices of elements St, . . . , Sn from S. The three basic results mentioned above correspond to (~, +, x* = -x), ([0, 00[, +, x* = x) and (No, +, n* = n). The purpose of this book is to provide a treatment of these positive definite functions on abelian semigroups with involution. In doing so we also discuss related topics such as negative definite functions, completely mono tone functions and Hoeffding-type inequalities. We view these subjects as important ingredients of harmonic analysis on semigroups. It has been our aim, simultaneously, to write a book which can serve as a textbook for an advanced graduate course, because we feel that the notion of positive definiteness is an important and basic notion which occurs in mathematics as often as the notion of a Hilbert space.

Semigroups in Geometrical Function Theory

Semigroups in Geometrical Function Theory PDF Author: D. Shoikhet
Publisher: Springer Science & Business Media
ISBN: 9401596328
Category : Mathematics
Languages : en
Pages : 231

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Book Description
Historically, complex analysis and geometrical function theory have been inten sively developed from the beginning of the twentieth century. They provide the foundations for broad areas of mathematics. In the last fifty years the theory of holomorphic mappings on complex spaces has been studied by many mathemati cians with many applications to nonlinear analysis, functional analysis, differential equations, classical and quantum mechanics. The laws of dynamics are usually presented as equations of motion which are written in the abstract form of a dy namical system: dx / dt + f ( x) = 0, where x is a variable describing the state of the system under study, and f is a vector function of x. The study of such systems when f is a monotone or an accretive (generally nonlinear) operator on the under lying space has been recently the subject of much research by analysts working on quite a variety of interesting topics, including boundary value problems, integral equations and evolution problems (see, for example, [19, 13] and [29]). In a parallel development (and even earlier) the generation theory of one parameter semigroups of holomorphic mappings in en has been the topic of interest in the theory of Markov stochastic processes and, in particular, in the theory of branching processes (see, for example, [63, 127, 48] and [69]).

Analysis on Semigroups

Analysis on Semigroups PDF Author: John F. Berglund
Publisher: Wiley-Interscience
ISBN:
Category : Mathematics
Languages : en
Pages : 360

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Book Description
This treatment of analysis on semigroups stresses the functional analytical and dynamical theory of continuous representations of semitopological semigroups. Topics covered include compact semitopological semigroups, invariant means and idempotent means on compact semitopological semigroups, affine compactifications, left multiplicatively continuous functions and weakly left continuous functions, compactifications of infinite direct products, and weakly almost periodic semigroups of Markov operators. Contains over 200 exercises, from simple applications and examples to further developments of the theory.

Groupoids, Inverse Semigroups, and their Operator Algebras

Groupoids, Inverse Semigroups, and their Operator Algebras PDF Author: Alan Paterson
Publisher: Springer Science & Business Media
ISBN: 1461217741
Category : Mathematics
Languages : en
Pages : 286

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Book Description
In recent years, it has become increasingly clear that there are important connections relating three concepts -- groupoids, inverse semigroups, and operator algebras. There has been a great deal of progress in this area over the last two decades, and this book gives a careful, up-to-date and reasonably extensive account of the subject matter. After an introductory first chapter, the second chapter presents a self-contained account of inverse semigroups, locally compact and r-discrete groupoids, and Lie groupoids. The section on Lie groupoids in chapter 2 contains a detailed discussion of groupoids particularly important in noncommutative geometry, including the holonomy groupoids of a foliated manifold and the tangent groupoid of a manifold. The representation theories of locally compact and r-discrete groupoids are developed in the third chapter, and it is shown that the C*-algebras of r-discrete groupoids are the covariance C*-algebras for inverse semigroup actions on locally compact Hausdorff spaces. A final chapter associates a universal r-discrete groupoid with any inverse semigroup. Six subsequent appendices treat topics related to those covered in the text. The book should appeal to a wide variety of professional mathematicians and graduate students in fields such as operator algebras, analysis on groupoids, semigroup theory, and noncommutative geometry. It will also be of interest to mathematicians interested in tilings and theoretical physicists whose focus is modeling quasicrystals with tilings. An effort has been made to make the book lucid and 'user friendly"; thus it should be accessible to any reader with a basic background in measure theory and functional analysis.

Numerical Semigroups and Applications

Numerical Semigroups and Applications PDF Author: Abdallah Assi
Publisher: Springer
ISBN: 3319413309
Category : Mathematics
Languages : en
Pages : 106

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Book Description
This work presents applications of numerical semigroups in Algebraic Geometry, Number Theory, and Coding Theory. Background on numerical semigroups is presented in the first two chapters, which introduce basic notation and fundamental concepts and irreducible numerical semigroups. The focus is in particular on free semigroups, which are irreducible; semigroups associated with planar curves are of this kind. The authors also introduce semigroups associated with irreducible meromorphic series, and show how these are used in order to present the properties of planar curves. Invariants of non-unique factorizations for numerical semigroups are also studied. These invariants are computationally accessible in this setting, and thus this monograph can be used as an introduction to Factorization Theory. Since factorizations and divisibility are strongly connected, the authors show some applications to AG Codes in the final section. The book will be of value for undergraduate students (especially those at a higher level) and also for researchers wishing to focus on the state of art in numerical semigroups research.

A Sequence of Problems on Semigroups

A Sequence of Problems on Semigroups PDF Author: john neuberger
Publisher: Springer Science & Business Media
ISBN: 1461404304
Category : Mathematics
Languages : en
Pages : 142

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Book Description
This text consists of a sequence of problems which develop a variety of aspects in the field of semigroupsof operators. Many of the problems are not found easily in other books. Written in the Socratic/Moore method, this is a problem book without the answers presented. To get the most out of the content requires high motivation from the reader to work out the exercises. The reader is given the opportunity to discover important developments of the subject and to quickly arrive at the point of independent research. The compactness of the volume and the reputation of the author lends this consider set of problems to be a 'classic' in the making. This text is highly recommended for us as supplementary material for 3 graduate level courses.

Advances in the Theory of Varieties of Semigroups

Advances in the Theory of Varieties of Semigroups PDF Author: Edmond W. H. Lee
Publisher: Springer Nature
ISBN: 3031164970
Category : Mathematics
Languages : en
Pages : 286

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Book Description
This monograph thoroughly explores the development of the theory of varieties of semigroups and of two related algebras: involution semigroups and monoids. Through this in-depth analysis, readers will attain a deeper understanding of the differences between these three types of varieties, which may otherwise seem counterintuitive. New results with detailed proofs are also presented that answer previously unsolved fundamental problems. Featuring both a comprehensive overview as well as highlighting the author’s own significant contributions to the area, this book will help establish this subfield as a matter of timely interest. Advances in the Theory of Varieties of Semigroups will appeal to researchers in universal algebra and will be particularly valuable for specialists in semigroups.

Functional Analysis and Semi-Groups

Functional Analysis and Semi-Groups PDF Author: Einar Hille
Publisher: Dutt Press
ISBN: 1443721670
Category : Mathematics
Languages : en
Pages : 542

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Book Description
AMERICAN MATHEMATICAL SOCIETY COLLOQUIUM PUBLICATIONS VOLUME XXXI FUNCTIONAL ANALYSIS AND SEMI-GROUPS BY EINAR HILLE PROFESSOR OF MATHEMATICS YALE UNIVERSITY PUBLISHED BY THE AMERICAN MATHEMATICAL SOCIETY 531 WEST 116iH STREET, NEW YORK CITY 1948 To KIRSTI And each man hears as the twilight nears, to the beat of his dying hearty The Devil drum on the darkened pane You did it, but was it Art FOREWORD The analytical theory of semi-groups is a recent addition to the ever-growing list of mathematical disciplines. It was my good fortune to take an early interest in this disci pline and to see it reach maturity. It has been a pleasant association I hail a semi-group when I see one and I seem to see them every where Friends have observed, however, that there are mathematical objects which are not semi-groups. The present book is an elaboration of my Colloquium Lectures delivered before the American Mathematical Society at its August, 1944 meeting at Wellesley College. I wish to thank the Society and its officers for their invitation to present and publish these lectures. The book is divided into three parts plus an appendix. My desire to give a practically self-contained presentation of the theory required the inclusion of an elaborate introduc tion to modern functional analysis with special emphasis on function theory in Banach spaces and algebras. This occupies Part One of the book and the Appendix these portions can be read separately from the rest and may be used as a text in a course on operator theory. It is possible to cover most of the material in these six chapters in two terms. The analytical theory of one-parameter semi-groups occupies Part Two while Part Three deals with theapplications to analysis. The latter include such varied topics as trigonometric series and integrals, summability, fractional integration, stochastic theory, and the problem of Cauchy for partial differential equations. In the general theory the reader will also find an alternate approach to ergodic theory. All semi-groups studied in this treatise are referred to a normed topology semi-groups without topology figure in a few places but no details are given. The task of developing an adequate theory of trans formation semi-groups operating in partially ordered spaces is left to more competent hands. The literature has been covered rather incompletely owing to recent war conditions and to the wide range of topics touched upon, which have made it exceedingly difficult to give the proper credits. This investigation has been supported by grants from the American Philosophical Society and from Yale University which are gratefully acknowledged. On the personal side, it is a great pleasure to express my gratitude to the many friends who have aided me in pre paring this book. J. D. Tamarkin, who read and criticized my early work in the field and who vigorously urged its inclusion in the Colloquium Series is beyond the reach of my grati tude. I am deeply indebted to Nelson Dunford and to Max Zorn who have contributed extensively to the book, the former chiefly to Chapters II, III, V, VIII, IX, and XIV, the latter to Chapters IV, VII, and XXII. Both have given me generously of their time and special experience. Various portions of the manuscript have been critically examined and amended by Warren Ambrose, E. G. Begle, H. Cramdr, J. L. Doob, W. Feller, N. Jacobson, D. S. Miller, II. Pollard, C.E. Rickart, and I. E. Segal. To all helpers, named and un named, I extend my warmest thanks. EINAK HILLE New Haven, Conn., December, 1946 CONVENTIONS Each Part of the book starts with a Summary, each Chapter with an Orientation. The chapters are divided into sections and the sections, except orientations, are grouped into paragraphs. Cross references are normally to sections, rarely to paragraphs. Section 3.10 is the tenth section of Chapter III it belongs to 2 which is referred to as 3.2 when necessary...