Functional Analysis And Semi Groups

Author : Einar Hille,Ralph Saul Phillips
Publisher : American Mathematical Soc.
Page : 808 pages
File Size : 54,8 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 : C. van den Berg,J. P. R. Christensen,P. Ressel
Publisher : Springer Science & Business Media
Page : 299 pages
File Size : 44,5 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 : Alfredo Lorenzi,Bernhard Ruf
Publisher : Birkhäuser
Page : 404 pages
File Size : 46,7 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 : John F. Berglund,Hugo D. Junghenn,Paul Milnes
Publisher : Wiley-Interscience
Page : 360 pages
File Size : 47,7 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 : 53,6 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 : Ioan I. Vrabie
Publisher : Elsevier
Page : 396 pages
File Size : 44,6 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.

Author : Kosaku Yosida
Publisher : Springer Science & Business Media
Page : 480 pages
File Size : 50,5 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9783662117910

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Functional Analysis by Kosaku Yosida Pdf

Author : Marius Tucsnak,George Weiss
Publisher : Springer Science & Business Media
Page : 488 pages
File Size : 55,6 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 : Amnon Pazy
Publisher : Springer Science & Business Media
Page : 289 pages
File Size : 54,6 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 : Kalyan B. Sinha,Sachi Srivastava
Publisher : Springer
Page : 169 pages
File Size : 43,9 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 : David Applebaum
Publisher : Cambridge University Press
Page : 235 pages
File Size : 45,7 Mb
Release : 2019-08-15
Category : Mathematics
ISBN : 9781108483094

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Semigroups of Linear Operators by David Applebaum Pdf

Provides a graduate-level introduction to the theory of semigroups of operators.

Author : Brunello Terreni
Publisher : Springer Science & Business Media
Page : 426 pages
File Size : 44,7 Mb
Release : 2002
Category : Mathematics
ISBN : 3764367911

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Evolution Equations, Semigroups and Functional Analysis by Brunello Terreni 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 : Klaus-Jochen Engel,Rainer Nagel
Publisher : Springer Science & Business Media
Page : 257 pages
File Size : 44,8 Mb
Release : 2006-06-06
Category : Mathematics
ISBN : 9780387313412

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A Short Course on Operator Semigroups by Klaus-Jochen Engel,Rainer Nagel Pdf

The book offers a direct and up-to-date introduction to the theory of one-parameter semigroups of linear operators on Banach spaces. The book is intended for students and researchers who want to become acquainted with the concept of semigroups.

Author : D. Shoikhet
Publisher : Springer Science & Business Media
Page : 231 pages
File Size : 45,6 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9789401596329

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Semigroups in Geometrical Function Theory by D. Shoikhet Pdf

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]).

Author : Edward Brian Davies
Publisher : Unknown
Page : 248 pages
File Size : 46,6 Mb
Release : 1980
Category : Functional analysis
ISBN : UCAL:B4497499

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One-parameter Semigroups by Edward Brian Davies Pdf