Semigroups of Linear Operators and Applications to Partial Differential EquationsSemigroups of Linear Operators and Applications to Partial 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: Amnon Pazy

Publisher: Springer Science & Business Media

ISBN: 9781461255611

Category:

Page: 282

View: 241

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.

Semigroups of Linear Operators and ApplicationsSemigroups of Linear Operators and Applications



Advanced graduate-level treatment of semigroup theory explores semigroups of linear operators and linear Cauchy problems. The text features challenging exercises and emphasizes motivation, heuristics, and further applications. 1985 edition.

Author: Jerome A. Goldstein

Publisher: Courier Dover Publications

ISBN: 9780486812571

Category:

Page: 320

View: 315

Advanced graduate-level treatment of semigroup theory explores semigroups of linear operators and linear Cauchy problems. The text features challenging exercises and emphasizes motivation, heuristics, and further applications. 1985 edition.

The Adjoint of a Semigroup of Linear OperatorsThe Adjoint of a Semigroup of Linear Operators



The book is addressed primarily to researchers working in semigroup theory, but in view of the "Banach space theory" flavour of many of the results, it will also be of interest to Banach space geometers and operator theorists.

Author: Jan van Neerven

Publisher: Springer

ISBN: 9783540474975

Category:

Page: 198

View: 553

This monograph provides a systematic treatment of the abstract theory of adjoint semigroups. After presenting the basic elementary results, the following topics are treated in detail: The sigma (X, X )-topology, -reflexivity, the Favard class, Hille-Yosida operators, interpolation and extrapolation, weak -continuous semigroups, the codimension of X in X , adjoint semigroups and the Radon-Nikodym property, tensor products of semigroups and duality, positive semigroups and multiplication semigroups. The major part of the material is reasonably self-contained and is accessible to anyone with basic knowledge of semi- group theory and Banach space theory. Most of the results are proved in detail. The book is addressed primarily to researchers working in semigroup theory, but in view of the "Banach space theory" flavour of many of the results, it will also be of interest to Banach space geometers and operator theorists.

The Asymptotic Behaviour of Semigroups of Linear OperatorsThe Asymptotic Behaviour of Semigroups of Linear Operators



This book presents a systematic account of the theory of asymptotic behaviour of semigroups of linear operators acting in a Banach space.

Author: Jan van Neerven

Publisher: Birkhäuser

ISBN: 9783034892063

Category:

Page: 241

View: 294

This book presents a systematic account of the theory of asymptotic behaviour of semigroups of linear operators acting in a Banach space. The focus is on the relationship between asymptotic behaviour of the semigroup and spectral properties of its infinitesimal generator. The most recent developments in the field are included, such as the Arendt-Batty-Lyubich-Vu theorem, the spectral mapp- ing theorem of Latushkin and Montgomery-Smith, Weis's theorem on stability of positive semigroup in Lp-spaces, the stability theorem for semigroups whose resolvent is bounded in a half-plane, and a systematic theory of individual stability. Addressed to researchers and graduate students with interest in the fields of operator semigroups and evolution equations, this book is self-contained and provides complete proofs.

Applied Nonlinear SemigroupsApplied Nonlinear Semigroups



The user-friendly presentation in the book is centred on Abstract Cauchy Problems which model various processes such as particle transport,diffusion and combustion, all of which are examples of systems which evolve with time.

Author: A. Belleni-Morante

Publisher: Wiley-Blackwell

ISBN: STANFORD:36105023416154

Category:

Page: 273

View: 522

Mathematical Methods in Practice Advisory Editors Bruno Brosowski Universität Frankfurt Germany Gary F. Roach University of Strathclyde UK Volume 3 Applied Nonlinear Semigroups A. Belleni-Morante University of Florence, Italy A. C. McBride University of Strathclyde, UK In many disciplines such as physics, chemistry, biology, meteorology, electronics and economics, it is increasingly necessary to develop mathematical models that describe how the state of a system evolves with time. A useful way of studying such a model is to recast the appropriate evolution equation as an Abstract Cauchy Problem (ACP), which can then be analysed via the powerful theory of semigroups of operators. The user-friendly presentation in the book is centred on Abstract Cauchy Problems which model various processes such as particle transport,diffusion and combustion, all of which are examples of systems which evolve with time. The authors provide an introduction to the requisite concepts from functional analysis before moving on to the theory of semigroups of linear operators and their application to linear ACPs. These ideas are then applied to semilinear problems and fully nonlinear problems and it is shown how results from the linear theory can be extended. Finally, a variety of applications of practical interest are included. By leading a non-expert to the solutions of problems involving evolution equations via the theory of semigroups of operators, both linear and nonlinear, the book provides an accessible introduction to the treatment of the subject. The reader is assumed to have a basic knowledge of real analysis and vector spaces. M.Sc. and graduate students of functional analysis, applied mathematics, physics and engineering will find this an invaluable introduction to the subject.

A Short Course on Operator SemigroupsA Short Course on Operator Semigroups



The book offers a direct and up-to-date introduction to the theory of one-parameter semigroups of linear operators on Banach spaces.

Author: Klaus-Jochen Engel

Publisher: Springer Science & Business Media

ISBN: 9780387313412

Category:

Page: 247

View: 706

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.

Semi Groups of Operators and ApproximationSemi Groups of Operators and Approximation



The aim of this book is to present a systematic treatment of semi groups of bounded linear operators on Banach spaces and their connec tions with approximation theoretical questions in a more classical setting as well as within the setting ...

Author: Paul Leo Butzer

Publisher: Springer Science & Business Media

ISBN: 9783642460661

Category:

Page: 322

View: 360

In recent years important progress has been made in the study of semi-groups of operators from the viewpoint of approximation theory. These advances have primarily been achieved by introducing the theory of intermediate spaces. The applications of the theory not only permit integration of a series of diverse questions from many domains of mathematical analysis but also lead to significant new results on classical approximation theory, on the initial and boundary behavior of solutions of partial differential equations, and on the theory of singular integrals. The aim of this book is to present a systematic treatment of semi groups of bounded linear operators on Banach spaces and their connec tions with approximation theoretical questions in a more classical setting as well as within the setting of the theory of intermediate spaces. However, no attempt is made to present an exhaustive account of the theory of semi-groups of operators per se, which is the central theme of the monumental treatise by HILLE and PHILLIPS (1957). Neither has it been attempted to give an account of the theory of approximation as such. A number of excellent books on various aspects of the latter theory has appeared in recent years, so for example CHENEY (1966), DAVIS (1963), LORENTZ (1966), MEINARDUS (1964), RICE (1964), SARD (1963). By contrast, the present book is primarily concerned with those aspects of semi-group theory that are connected in some way or other with approximation.

Generators of Strongly Continuous SemigroupsGenerators of Strongly Continuous Semigroups



This work will be useful both for those undertaking research as well as for graduate students; a basic knowledge of functional analysis and probability theory are the only prerequisites.

Author: J. A. van Casteren

Publisher: Addison-Wesley

ISBN: UCAL:B4405482

Category:

Page: 203

View: 158

This research note contains some recent results in the theory of strongly continuous semigroups of linear operators. Topics covered include the Feynman-Kac formalism with applications to Schrödinger operators, positivity preserving semigroups, quadratic form theory, holomorphic semigroups and bounded one-parameter groups. An appendix deals with some aspects of Feynman path integrals. A number of previously inaccessible results in semigroup theory are presented with full proofs. This work will be useful both for those undertaking research as well as for graduate students; a basic knowledge of functional analysis and probability theory are the only prerequisites.

One Parameter Semigroups for Linear Evolution EquationsOne Parameter Semigroups for Linear Evolution Equations



This book explores the theory of strongly continuous one-parameter semigroups of linear operators.

Author: Klaus-Jochen Engel

Publisher: Springer Science & Business Media

ISBN: 9780387226422

Category:

Page: 589

View: 819

This book explores the theory of strongly continuous one-parameter semigroups of linear operators. A special feature of the text is an unusually wide range of applications such as to ordinary and partial differential operators, to delay and Volterra equations, and to control theory. Also, the book places an emphasis on philosophical motivation and the historical background.

Semigroups of Linear and Nonlinear Operations and ApplicationsSemigroups of Linear and Nonlinear Operations and Applications



This is the first publication which follows an agreement by Kluwer Publishers with the Caribbean Mathematics Foundation (CMF), to publish the proceedings of its mathematical activities.

Author: Gisèle Ruiz Goldstein

Publisher: Springer Science & Business Media

ISBN: 9789401118880

Category:

Page: 283

View: 791

This is the first publication which follows an agreement by Kluwer Publishers with the Caribbean Mathematics Foundation (CMF), to publish the proceedings of its mathematical activities. To which one should add a disclaimer of sorts, namely that this volume is not the first in a series, because it is not first, and be cause neither party to the agreement construes these publications as elements of a series. Like the work of CMF, the arrangement between it and Kluwer Publishers, evolved gradually, empirically. CMF was created in 1988, and inaugurated with a conference on Ordered Algebraic Structures. Every year since there have been gatherings on a variety of mathematical topics: Locales and Topological Groups in 1989; Positive Operators in 1990; Finite Geometry and Abelian Groups in 1991; Semigroups of Operators last year. It should be stressed, however that in preparing for the first conference, there was no plan which might have augured what came after. One could say that one thing led to another, and one would be right enough.

Positive Semigroups of Operators and ApplicationsPositive Semigroups of Operators and Applications



This means that semigroup theory may be applied directly to the study of the equation I'!.f = h on M. In [45] Yau proves that, for h ~ 0, there are no nonconstant, nonnegative solutions f in [j' for 1

Author: O. Bratteli

Publisher: Springer Science & Business Media

ISBN: 9789400964846

Category:

Page: 202

View: 907

This means that semigroup theory may be applied directly to the study of the equation I'!.f = h on M. In [45] Yau proves that, for h ~ 0, there are no nonconstant, nonnegative solutions f in [j' for 1