Semigroups Of Operators And Spectral Theory

Author : S Kantorovitz
Publisher : CRC Press
Page : 156 pages
File Size : 40,9 Mb
Release : 1995-06-19
Category : Mathematics
ISBN : 0582277787

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Semigroups of Operators and Spectral Theory by S Kantorovitz Pdf

This book presents some aspects of the theory of semigroups of operators, mostly from the point of view of its interaction withspectral theory. In order to make it self-contained, a concise description of the basic theory of semigroups, with complete proofs, is included in Part I. Some of the author's recent results, such as the construction of the Hille-Yosida space for general operators, the semi-simplicity manifold, and a Taylor formula for semigroups as functions of their generator, are also included in Part I. Part II describes recent generalizations (most of them in bookform for the first time), including pre-semigroups, semi-simplicity manifolds in situations more general than that considered in Part I, semigroups of unbounded symmetric operators, and an analogous result on "local cosine families" and semi-analytic vectors. It is hoped that this book will inspire more research in this field. This book will be of particular interest to graduate students and researchers working operator theory and its applications.

Author : Klaus-Jochen Engel,Rainer Nagel
Publisher : Springer Science & Business Media
Page : 257 pages
File Size : 42,9 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 : Shmuel Kantorovitz
Publisher : Halsted Press
Page : 135 pages
File Size : 53,5 Mb
Release : 1995
Category : Semigroups of operators
ISBN : 0470235616

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Semigroups of Operators and Spectral Theory by Shmuel Kantorovitz Pdf

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 : 46,8 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 : Michael Demuth,Jan A. van Casteren
Publisher : Birkhäuser
Page : 476 pages
File Size : 54,7 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9783034884600

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Stochastic Spectral Theory for Selfadjoint Feller Operators by Michael Demuth,Jan A. van Casteren Pdf

In this book, a beautiful interplay between probability theory (Markov processes, martingale theory) on the one hand and operator and spectral theory on the other yields a uniform treatment of several kinds of Hamiltonians such as the Laplace operator, relativistic Hamiltonian, Laplace-Beltrami operator, and generators of Ornstein-Uhlenbeck processes. The unified approach provides a new viewpoint of and a deeper insight into the subject.

Author : Abram Iezekiilovich Plesner
Publisher : Unknown
Page : 256 pages
File Size : 54,9 Mb
Release : 1969
Category : Mathematics
ISBN : UOM:39015017325815

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Spectral Theory of Linear Operators by Abram Iezekiilovich Plesner Pdf

Author : Jan van Neerven
Publisher : Birkhäuser
Page : 247 pages
File Size : 45,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034892063

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The Asymptotic Behaviour of Semigroups of Linear Operators by Jan van Neerven Pdf

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.

Author : András Bátkai,Marjeta Kramar Fijavž,Abdelaziz Rhandi
Publisher : Birkhäuser
Page : 364 pages
File Size : 42,6 Mb
Release : 2017-02-13
Category : Mathematics
ISBN : 9783319428130

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Positive Operator Semigroups by András Bátkai,Marjeta Kramar Fijavž,Abdelaziz Rhandi Pdf

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 : Gisele Ruiz Goldstein,Rainer Nagel,Silvia Romanelli
Publisher : CRC Press
Page : 267 pages
File Size : 47,6 Mb
Release : 2019-04-24
Category : Mathematics
ISBN : 9780429530050

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Evolution Equations by Gisele Ruiz Goldstein,Rainer Nagel,Silvia Romanelli Pdf

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

Author : E. Brian Davies
Publisher : Cambridge University Press
Page : 436 pages
File Size : 48,9 Mb
Release : 2007-04-26
Category : Mathematics
ISBN : 9781139464338

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Linear Operators and their Spectra by E. Brian Davies Pdf

This wide ranging but self-contained account of the spectral theory of non-self-adjoint linear operators is ideal for postgraduate students and researchers, and contains many illustrative examples and exercises. Fredholm theory, Hilbert-Schmidt and trace class operators are discussed, as are one-parameter semigroups and perturbations of their generators. Two chapters are devoted to using these tools to analyze Markov semigroups. The text also provides a thorough account of the new theory of pseudospectra, and presents the recent analysis by the author and Barry Simon of the form of the pseudospectra at the boundary of the numerical range. This was a key ingredient in the determination of properties of the zeros of certain orthogonal polynomials on the unit circle. Finally, two methods, both very recent, for obtaining bounds on the eigenvalues of non-self-adjoint Schrodinger operators are described. The text concludes with a description of the surprising spectral properties of the non-self-adjoint harmonic oscillator.

Author : Shmuel Kantorovitz
Publisher : Springer Science & Business Media
Page : 266 pages
File Size : 51,8 Mb
Release : 2009-10-22
Category : Mathematics
ISBN : 9780817649326

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Topics in Operator Semigroups by Shmuel Kantorovitz Pdf

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 : Fengyu Wang
Publisher : Elsevier
Page : 391 pages
File Size : 46,8 Mb
Release : 2006-04-06
Category : Mathematics
ISBN : 9780080532073

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Functional Inequalities Markov Semigroups and Spectral Theory by Fengyu Wang Pdf

In this book, the functional inequalities are introduced to describe:(i) the spectrum of the generator: the essential and discrete spectrums, high order eigenvalues, the principle eigenvalue, and the spectral gap;(ii) the semigroup properties: the uniform intergrability, the compactness, the convergence rate, and the existence of density;(iii) the reference measure and the intrinsic metric: the concentration, the isoperimetic inequality, and the transportation cost inequality.

Author : Carlos S. Kubrusly
Publisher : Springer Science & Business Media
Page : 203 pages
File Size : 46,6 Mb
Release : 2012-06-01
Category : Mathematics
ISBN : 9780817683283

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Spectral Theory of Operators on Hilbert Spaces by Carlos S. Kubrusly Pdf

This work is a concise introduction to spectral theory of Hilbert space operators. Its emphasis is on recent aspects of theory and detailed proofs, with the primary goal of offering a modern introductory textbook for a first graduate course in the subject. The coverage of topics is thorough, as the book explores various delicate points and hidden features often left untreated. Spectral Theory of Operators on Hilbert Spaces is addressed to an interdisciplinary audience of graduate students in mathematics, statistics, economics, engineering, and physics. It will also be useful to working mathematicians using spectral theory of Hilbert space operators, as well as for scientists wishing to apply spectral theory to their field. ​

Author : Jerome A. Goldstein
Publisher : Courier Dover Publications
Page : 320 pages
File Size : 50,5 Mb
Release : 2017-05-17
Category : Mathematics
ISBN : 9780486822228

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Semigroups of Linear Operators and Applications by Jerome A. Goldstein Pdf

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 : Vladimir Müller
Publisher : Springer Science & Business Media
Page : 439 pages
File Size : 51,9 Mb
Release : 2007-12-24
Category : Mathematics
ISBN : 9783764382650

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Spectral Theory of Linear Operators by Vladimir Müller Pdf

This book is dedicated to the spectral theory of linear operators on Banach spaces and of elements in Banach algebras. It presents a survey of results concerning various types of spectra, both of single and n-tuples of elements. Typical examples are the one-sided spectra, the approximate point, essential, local and Taylor spectrum, and their variants. Many results appear here for the first time in a monograph.