Analysis On Semigroups

Author : C. van den Berg,J. P. R. Christensen,P. Ressel
Publisher : Springer Science & Business Media
Page : 299 pages
File Size : 52,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461211280

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Harmonic Analysis on Semigroups by C. van den Berg,J. P. R. Christensen,P. Ressel Pdf

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.

Author : Einar Hille,Ralph Saul Phillips
Publisher : American Mathematical Soc.
Page : 808 pages
File Size : 54,7 Mb
Release : 1996-02-06
Category : Banach algebras
ISBN : 9780821810316

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Functional Analysis and Semi-groups by Einar Hille,Ralph Saul Phillips Pdf

Early in 1952 it became obvious that a new printing would be needed, and new advances in the theory called for extensive revision. It has been completely rewritten, mostly by Phillips, and much has been added while keeping the existing framework. Thus, the algebraic tools play a major role, and are introduced early, leading to a more satisfactory operational calculus and spectral theory. The Laplace-Stieltjes transform methods, used by Hille, have not been replaced but rather supplemented by the new tools. - Foreword.

Author : John F. Berglund,Hugo D. Junghenn,Paul Milnes
Publisher : Wiley-Interscience
Page : 360 pages
File Size : 49,8 Mb
Release : 1989
Category : Mathematics
ISBN : UCAL:B5008603

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Analysis on Semigroups by John F. Berglund,Hugo D. Junghenn,Paul Milnes Pdf

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.

Author : John F. Berglund,Hugo D. Junghenn,Paul Milnes
Publisher : Wiley-Interscience
Page : 360 pages
File Size : 46,9 Mb
Release : 1989-05-03
Category : Mathematics
ISBN : UCAL:B4359771

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Analysis on Semigroups by John F. Berglund,Hugo D. Junghenn,Paul Milnes Pdf

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.

Author : Kalyan B. Sinha,Sachi Srivastava
Publisher : Springer
Page : 169 pages
File Size : 45,5 Mb
Release : 2017-07-12
Category : Mathematics
ISBN : 9789811048647

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Theory of Semigroups and Applications by Kalyan B. Sinha,Sachi Srivastava Pdf

The book presents major topics in semigroups, such as operator theory, partial differential equations, harmonic analysis, probability and statistics and classical and quantum mechanics, and applications. Along with a systematic development of the subject, the book emphasises on the explorations of the contact areas and interfaces, supported by the presentations of explicit computations, wherever feasible. Designed into seven chapters and three appendixes, the book targets to the graduate and senior undergraduate students of mathematics, as well as researchers in the respective areas. The book envisages the pre-requisites of a good understanding of real analysis with elements of the theory of measures and integration, and a first course in functional analysis and in the theory of operators. Chapters 4 through 6 contain advanced topics, which have many interesting applications such as the Feynman–Kac formula, the central limit theorem and the construction of Markov semigroups. Many examples have been given in each chapter, partly to initiate and motivate the theory developed and partly to underscore the applications. The choice of topics in this vastly developed book is a difficult one, and the authors have made an effort to stay closer to applications instead of bringing in too many abstract concepts.

Author : Amnon Pazy
Publisher : Springer Science & Business Media
Page : 289 pages
File Size : 48,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461255611

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Semigroups of Linear Operators and Applications to Partial Differential Equations by Amnon Pazy Pdf

Since the characterization of generators of C0 semigroups was established in the 1940s, semigroups of linear operators and its neighboring areas have developed into an abstract theory that has become a necessary discipline in functional analysis and differential equations. This book presents that theory and its basic applications, and the last two chapters give a connected account of the applications to partial differential equations.

Author : A.V. Balakrishnan
Publisher : Springer Science & Business Media
Page : 386 pages
File Size : 40,7 Mb
Release : 2000-08-01
Category : Mathematics
ISBN : 376436310X

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Semigroups of Operators: Theory and Applications by A.V. Balakrishnan Pdf

These Proceedings comprise the bulk of the papers presented at the Inter national Conference on Semigroups of Opemtors: Theory and Contro~ held 14-18 December 1998, Newport Beach, California, U.S.A. The intent of the Conference was to highlight recent advances in the the ory of Semigroups of Operators which provides the abstract framework for the time-domain solutions of time-invariant boundary-value/initial-value problems of partial differential equations. There is of course a firewall between the ab stract theory and the applications and one of the Conference aims was to bring together both in the hope that it may be of value to both communities. In these days when all scientific activity is judged by its value on "dot com" it is not surprising that mathematical analysis that holds no promise of an immediate commercial product-line, or even a software tool-box, is not high in research priority. We are particularly pleased therefore that the National Science Foundation provided generous financial support without which this Conference would have been impossible to organize. Our special thanks to Dr. Kishan Baheti, Program Manager.

Author : Alfredo Lorenzi,Bernhard Ruf
Publisher : Birkhäuser
Page : 404 pages
File Size : 49,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034882217

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Evolution Equations, Semigroups and Functional Analysis by Alfredo Lorenzi,Bernhard Ruf Pdf

Brunello Terreni (1953-2000) was a researcher and teacher with vision and dedication. The present volume is dedicated to the memory of Brunello Terreni. His mathematical interests are reflected in 20 expository articles written by distinguished mathematicians. The unifying theme of the articles is "evolution equations and functional analysis", which is presented in various and diverse forms: parabolic equations, semigroups, stochastic evolution, optimal control, existence, uniqueness and regularity of solutions, inverse problems as well as applications. Contributors: P. Acquistapace, V. Barbu, A. Briani, L. Boccardo, P. Colli Franzone, G. Da Prato, D. Donatelli, A. Favini, M. Fuhrmann, M. Grasselli, R. Illner, H. Koch, R. Labbas, H. Lange, I. Lasiecka, A. Lorenzi, A. Lunardi, P. Marcati, R. Nagel, G. Nickel, V. Pata, M. M. Porzio, B. Ruf, G. Savaré, R. Schnaubelt, E. Sinestrari, H. Tanabe, H. Teismann, E. Terraneo, R. Triggiani, A. Yagi.

Author : Filippo Bracci,Manuel D. Contreras,Santiago Díaz-Madrigal
Publisher : Springer Nature
Page : 582 pages
File Size : 55,6 Mb
Release : 2020-02-14
Category : Mathematics
ISBN : 9783030367824

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Continuous Semigroups of Holomorphic Self-maps of the Unit Disc by Filippo Bracci,Manuel D. Contreras,Santiago Díaz-Madrigal Pdf

The book faces the interplay among dynamical properties of semigroups, analytical properties of infinitesimal generators and geometrical properties of Koenigs functions. The book includes precise descriptions of the behavior of trajectories, backward orbits, petals and boundary behavior in general, aiming to give a rather complete picture of all interesting phenomena that occur. In order to fulfill this task, we choose to introduce a new point of view, which is mainly based on the intrinsic dynamical aspects of semigroups in relation with the hyperbolic distance and a deep use of Carathéodory prime ends topology and Gromov hyperbolicity theory. This work is intended both as a reference source for researchers interested in the subject, and as an introductory book for beginners with a (undergraduate) background in real and complex analysis. For this purpose, the book is self-contained and all non-standard (and, mostly, all standard) results are proved in details.

Author : Abdallah Assi,Pedro A. García-Sánchez
Publisher : Springer
Page : 106 pages
File Size : 46,8 Mb
Release : 2016-08-25
Category : Mathematics
ISBN : 9783319413303

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Numerical Semigroups and Applications by Abdallah Assi,Pedro A. García-Sánchez Pdf

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.

Author : Marius Tucsnak,George Weiss
Publisher : Springer Science & Business Media
Page : 488 pages
File Size : 54,7 Mb
Release : 2009-03-13
Category : Mathematics
ISBN : 9783764389932

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Observation and Control for Operator Semigroups by Marius Tucsnak,George Weiss Pdf

This book studies observation and control operators for linear systems where the free evolution of the state can be described by an operator semigroup on a Hilbert space. It includes a large number of examples coming mostly from partial differential equations.

Author : Wolfgang Arendt,Rainer Nagel,Annette Grabosch,Günther Greiner,Ulrich Groh,Heinrich P. Lotz,Ulrich Moustakas,Frank Neubrander,Ulf Schlotterbeck
Publisher : Springer
Page : 468 pages
File Size : 47,6 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540397915

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One-parameter Semigroups of Positive Operators by Wolfgang Arendt,Rainer Nagel,Annette Grabosch,Günther Greiner,Ulrich Groh,Heinrich P. Lotz,Ulrich Moustakas,Frank Neubrander,Ulf Schlotterbeck Pdf

Author : Alan Paterson
Publisher : Springer Science & Business Media
Page : 286 pages
File Size : 45,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461217749

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Groupoids, Inverse Semigroups, and their Operator Algebras by Alan Paterson Pdf

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.

Author : Tanja Eisner
Publisher : Birkhäuser
Page : 208 pages
File Size : 45,7 Mb
Release : 2019-10-01
Category : Mathematics
ISBN : 9783034601955

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Stability of Operators and Operator Semigroups by Tanja Eisner Pdf

The asymptotic behaviour, in particular "stability" in some sense, is studied systematically for discrete and for continuous linear dynamical systems on Banach spaces. Of particular concern is convergence to an equilibrium with respect to various topologies. Parallels and differences between the discrete and the continuous situation are emphasised.

Author : Ioan I. Vrabie
Publisher : Elsevier
Page : 386 pages
File Size : 42,5 Mb
Release : 2003-03-21
Category : Mathematics
ISBN : 9780080530048

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Co-Semigroups and Applications by Ioan I. Vrabie Pdf

The book contains a unitary and systematic presentation of both classical and very recent parts of a fundamental branch of functional analysis: linear semigroup theory with main emphasis on examples and applications. There are several specialized, but quite interesting, topics which didn't find their place into a monograph till now, mainly because they are very new. So, the book, although containing the main parts of the classical theory of Co-semigroups, as the Hille-Yosida theory, includes also several very new results, as for instance those referring to various classes of semigroups such as equicontinuous, compact, differentiable, or analytic, as well as to some nonstandard types of partial differential equations, i.e. elliptic and parabolic systems with dynamic boundary conditions, and linear or semilinear differential equations with distributed (time, spatial) measures. Moreover, some finite-dimensional-like methods for certain semilinear pseudo-parabolic, or hyperbolic equations are also disscussed. Among the most interesting applications covered are not only the standard ones concerning the Laplace equation subject to either Dirichlet, or Neumann boundary conditions, or the Wave, or Klein-Gordon equations, but also those referring to the Maxwell equations, the equations of Linear Thermoelasticity, the equations of Linear Viscoelasticity, to list only a few. Moreover, each chapter contains a set of various problems, all of them completely solved and explained in a special section at the end of the book. The book is primarily addressed to graduate students and researchers in the field, but it would be of interest for both physicists and engineers. It should be emphasised that it is almost self-contained, requiring only a basic course in Functional Analysis and Partial Differential Equations.