A Short Course On Operator Semigroups

Author : Klaus-Jochen Engel
Publisher : Springer Science & Business Media
ISBN 13 : 0387313419
Total Pages : 257 pages
Book Rating : 4.12/5 ( download)

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Download or read book A Short Course on Operator Semigroups written by Klaus-Jochen Engel and published by Springer Science & Business Media. This book was released on 2006-06-06 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : András Bátkai
Publisher : Birkhäuser
ISBN 13 : 3319428136
Total Pages : 364 pages
Book Rating : 4.30/5 ( download)

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Download or read book Positive Operator Semigroups written by András Bátkai and published by Birkhäuser. This book was released on 2017-02-13 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Shmuel Kantorovitz
Publisher : Springer Science & Business Media
ISBN 13 : 0817649328
Total Pages : 266 pages
Book Rating : 4.26/5 ( download)

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Download or read book Topics in Operator Semigroups written by Shmuel Kantorovitz and published by Springer Science & Business Media. This book was released on 2009-10-22 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Marat V. Markin
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110600986
Total Pages : 425 pages
Book Rating : 4.88/5 ( download)

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Download or read book Elementary Operator Theory written by Marat V. Markin and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-04-06 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is intended as a text for a one-semester graduate course in operator theory to be taught "from scratch'', not as a sequel to a functional analysis course, with the basics of the spectral theory of linear operators taking the center stage. The book consists of six chapters and appendix, with the material flowing from the fundamentals of abstract spaces (metric, vector, normed vector, and inner product), the Banach Fixed-Point Theorem and its applications, such as Picard's Existence and Uniqueness Theorem, through the basics of linear operators, two of the three fundamental principles (the Uniform Boundedness Principle and the Open Mapping Theorem and its equivalents: the Inverse Mapping and Closed Graph Theorems), to the elements of the spectral theory, including Gelfand's Spectral Radius Theorem and the Spectral Theorem for Compact Self-Adjoint Operators, and its applications, such as the celebrated Lyapunov Stability Theorem. Conceived as a text to be used in a classroom, the book constantly calls for the student's actively mastering the knowledge of the subject matter. There are problems at the end of each chapter, starting with Chapter 2 and totaling at 150. Many important statements are given as problems and frequently referred to in the main body. There are also 432 Exercises throughout the text, including Chapter 1 and the Appendix, which require of the student to prove or verify a statement or an example, fill in certain details in a proof, or provide an intermediate step or a counterexample. They are also an inherent part of the material. More difficult problems are marked with an asterisk, many problems and exercises are supplied with "existential'' hints. The book is generous on Examples and contains numerous Remarks accompanying definitions, examples, and statements to discuss certain subtleties, raise questions on whether the converse assertions are true, whenever appropriate, or whether the conditions are essential. With carefully chosen material, proper attention given to applications, and plenty of examples, problems, and exercises, this well-designed text is ideal for a one-semester Master's level graduate course in operator theory with emphasis on spectral theory for students majoring in mathematics, physics, computer science, and engineering. Contents Preface Preliminaries Metric Spaces Vector Spaces, Normed Vector Spaces, and Banach Spaces Linear Operators Elements of Spectral Theory in a Banach Space Setting Elements of Spectral Theory in a Hilbert Space Setting Appendix: The Axiom of Choice and Equivalents Bibliography Index

Author : Lin Chin-yuan
Publisher : World Scientific
ISBN 13 : 9814616400
Total Pages : 176 pages
Book Rating : 4.09/5 ( download)

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Download or read book An Exponential Function Approach To Parabolic Equations written by Lin Chin-yuan and published by World Scientific. This book was released on 2014-08-08 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is on initial-boundary value problems for parabolic partial differential equations of second order. It rewrites the problems as abstract Cauchy problems or evolution equations, and then solves them by the technique of elementary difference equations. Because of this, the volume assumes less background and provides an easy approach for readers to understand.

Author : Eder Kikianty
Publisher : Springer Nature
ISBN 13 : 3030709744
Total Pages : 321 pages
Book Rating : 4.47/5 ( download)

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Download or read book Positivity and its Applications written by Eder Kikianty and published by Springer Nature. This book was released on 2021-07-22 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings volume features selected contributions from the conference Positivity X. The field of positivity deals with ordered mathematical structures and their applications. At the biannual series of Positivity conferences, the latest developments in this diverse field are presented. The 2019 edition was no different, with lectures covering a broad spectrum of topics, including vector and Banach lattices and operators on such spaces, abstract stochastic processes in an ordered setting, the theory and applications of positive semi-groups to partial differential equations, Hilbert geometries, positivity in Banach algebras and, in particular, operator algebras, as well as applications to mathematical economics and financial mathematics. The contributions in this book reflect the variety of topics discussed at the conference. They will be of interest to researchers in functional analysis, operator theory, measure and integration theory, operator algebras, and economics. Positivity X was dedicated to the memory of our late colleague and friend, Coenraad Labuschagne. His untimely death in 2018 came as an enormous shock to the Positivity community. He was a prominent figure in the Positivity community and was at the forefront of the recent development of abstract stochastic processes in a vector lattice context.

Author : Marius Tucsnak
Publisher : Springer Science & Business Media
ISBN 13 : 3764389931
Total Pages : 488 pages
Book Rating : 4.32/5 ( download)

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Download or read book Observation and Control for Operator Semigroups written by Marius Tucsnak and published by Springer Science & Business Media. This book was released on 2009-03-13 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Z Liu
Publisher : CRC Press
ISBN 13 : 9780849306150
Total Pages : 228 pages
Book Rating : 4.59/5 ( download)

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Download or read book Semigroups Associated with Dissipative Systems written by Z Liu and published by CRC Press. This book was released on 1999-01-29 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: Motivated by applications to control theory and to the theory of partial differential equations (PDE's), the authors examine the exponential stability and analyticity of C0-semigroups associated with various dissipative systems. They present a unique, systematic approach in which they prove exponential stability by combining a theory from semigroup theory with partial differential equation techniques, and use an analogous theorem with PDE techniques to prove analyticity. The result is a powerful but simple tool useful in determining whether these properties will preserve for a given dissipative system. The authors show that the exponential stability is preserved for all the mechanical systems considered in this book-linear, one-dimensional thermoelastic, viscoelastic and thermoviscoelastic systems, plus systems with shear or friction damping. However, readers also learn that this property does not hold true for linear three-dimensional systems without making assumptions on the domain and initial data, and that analyticity is a more sensitive property, not preserved even for some of the systems addressed in this study.

Author : Valentin A. Zagrebnov
Publisher : Springer Nature
ISBN 13 : 303156720X
Total Pages : 879 pages
Book Rating : 4.09/5 ( download)

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Download or read book Trotter-Kato Product Formulæ written by Valentin A. Zagrebnov and published by Springer Nature. This book was released on with total page 879 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Gisele Ruiz Goldstein
Publisher : CRC Press
ISBN 13 : 0429530056
Total Pages : 267 pages
Book Rating : 4.50/5 ( download)

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Download or read book Evolution Equations written by Gisele Ruiz Goldstein and published by CRC Press. This book was released on 2019-04-24 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 li