Topics In Operator Semigroups
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Topics In Operator Semigroups
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Author : Shmuel Kantorovitz
language : en
Publisher: Birkhäuser
Release Date : 2009-12-01
Topics In Operator Semigroups written by Shmuel Kantorovitz and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-12-01 with Mathematics categories.
This monograph is concerned with the interplay between the theory of operator semigroups and spectral theory. The basics on operator semigroups are concisely covered in this self-contained text. Part I deals with the Hille--Yosida and Lumer--Phillips characterizations of semigroup generators, the Trotter--Kato approximation theorem, Kato’s unified treatment of the exponential formula and the Trotter product formula, the Hille--Phillips perturbation theorem, and Stone’s representation of unitary semigroups. Part II explores generalizations of spectral theory’s connection to operator semigroups.
A Short Course On Operator Semigroups
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Author : Klaus-Jochen Engel
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-06-06
A Short Course On Operator Semigroups written by Klaus-Jochen Engel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-06-06 with Mathematics categories.
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.
Stability Of Operators And Operator Semigroups
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Author : Tanja Eisner
language : en
Publisher: Birkhäuser
Release Date : 2019-10-01
Stability Of Operators And Operator Semigroups written by Tanja Eisner and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-01 with Mathematics categories.
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.
Observation And Control For Operator Semigroups
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Author : Marius Tucsnak
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-03-13
Observation And Control For Operator Semigroups written by Marius Tucsnak and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-03-13 with Mathematics categories.
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.
Positive Operator Semigroups
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Author : András Bátkai
language : en
Publisher: Birkhäuser
Release Date : 2017-02-13
Positive Operator Semigroups written by András Bátkai and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-02-13 with Mathematics categories.
This book gives a gentle but up-to-date introduction into the theory of operator semigroups (or linear dynamical systems), which can be used with great success to describe the dynamics of complicated phenomena arising in many applications. Positivity is a property which naturally appears in physical, chemical, biological or economic processes. It adds a beautiful and far reaching mathematical structure to the dynamical systems and operators describing these processes. In the first part, the finite dimensional theory in a coordinate-free way is developed, which is difficult to find in literature. This is a good opportunity to present the main ideas of the Perron-Frobenius theory in a way which can be used in the infinite dimensional situation. Applications to graph matrices, age structured population models and economic models are discussed. The infinite dimensional theory of positive operator semigroups with their spectral and asymptotic theory is developed in the second part. Recent applications illustrate the theory, like population equations, neutron transport theory, delay equations or flows in networks. Each chapter is accompanied by a large set of exercises. An up-to-date bibliography and a detailed subject index help the interested reader. The book is intended primarily for graduate and master students. The finite dimensional part, however, can be followed by an advanced bachelor with a solid knowledge of linear algebra and calculus.
Semigroups Of Linear Operators And Applications To Partial Differential Equations
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Author : Amnon Pazy
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Semigroups Of Linear Operators And Applications To Partial Differential Equations written by Amnon Pazy and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
From the reviews: "Since E. Hille and K. Yoshida established the characterization of generators of C0 semigroups in the 1940s, semigroups of linear operators and its neighboring areas have developed into a beautiful abstract theory. Moreover, the fact that mathematically this abstract theory has many direct and important applications in partial differential equations enhances its importance as a necessary discipline in both functional analysis and differential equations. In my opinion Pazy has done an outstanding job in presenting both the abstract theory and basic applications in a clear and interesting manner. The choice and order of the material, the clarity of the proofs, and the overall presentation make this an excellent place for both researchers and students to learn about C0 semigroups." #Bulletin Applied Mathematical Sciences 4/85#1 "In spite of the other monographs on the subject, the reviewer can recommend that of Pazy as being particularly written, with a bias noticeably different from that of the other volumes. Pazy's decision to give a connected account of the applications to partial differential equations in the last two chapters was a particularly happy one, since it enables one to see what the theory can achieve much better than would the insertion of occasional examples. The chapters achieve a very nice balance between being so easy as to appear disappointing, and so sophisticated that they are incomprehensible except to the expert." #Bulletin of the London Mathematical Society#2
Evolution Equations
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Author : Gisele Ruiz Goldstein
language : en
Publisher: CRC Press
Release Date : 2003-06-24
Evolution Equations written by Gisele Ruiz Goldstein and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-06-24 with Mathematics categories.
Celebrating the work of renowned mathematician Jerome A. Goldstein, this reference compiles original research on the theory and application of evolution equations to stochastics, physics, engineering, biology, and finance. The text explores a wide range of topics in linear and nonlinear semigroup theory, operator theory, functional analysis, and linear and nonlinear partial differential equations, and studies the latest theoretical developments and uses of evolution equations in a variety of disciplines. Providing nearly 500 references, the book contains discussions by renowned mathematicians such as H. Brezis, G. Da Prato, N.E. Gretskij, I. Lasiecka, Peter Lax, M. M. Rao, and R. Triggiani.
One Parameter Semigroups Of Positive Operators
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Author : Wolfgang Arendt
language : en
Publisher: Springer
Release Date : 2006-11-14
One Parameter Semigroups Of Positive Operators written by Wolfgang Arendt and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
Semigroups Of Linear Operators
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Author : David Applebaum
language : en
Publisher: Cambridge University Press
Release Date : 2019-08-15
Semigroups Of Linear Operators written by David Applebaum and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-15 with Mathematics categories.
The theory of semigroups of operators is one of the most important themes in modern analysis. Not only does it have great intellectual beauty, but also wide-ranging applications. In this book the author first presents the essential elements of the theory, introducing the notions of semigroup, generator and resolvent, and establishes the key theorems of Hille–Yosida and Lumer–Phillips that give conditions for a linear operator to generate a semigroup. He then presents a mixture of applications and further developments of the theory. This includes a description of how semigroups are used to solve parabolic partial differential equations, applications to Levy and Feller–Markov processes, Koopmanism in relation to dynamical systems, quantum dynamical semigroups, and applications to generalisations of the Riemann–Liouville fractional integral. Along the way the reader encounters several important ideas in modern analysis including Sobolev spaces, pseudo-differential operators and the Nash inequality.
Theory Of Semigroups And Applications
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Author : Kalyan B. Sinha
language : en
Publisher: Springer
Release Date : 2017-07-12
Theory Of Semigroups And Applications written by Kalyan B. Sinha and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-12 with Mathematics categories.
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.