The Asymptotic Behaviour Of Semigroups Of Linear Operators PDF Download
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Author | : Jan van Neerven |
Publisher | : Birkhäuser |
Total Pages | : 247 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3034892063 |
Download The Asymptotic Behaviour of Semigroups of Linear Operators Book in PDF, ePub and Kindle
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 | : Eduard Yu. Emel'yanov |
Publisher | : Springer Science & Business Media |
Total Pages | : 181 |
Release | : 2007-02-17 |
Genre | : Mathematics |
ISBN | : 3764381140 |
Download Non-spectral Asymptotic Analysis of One-Parameter Operator Semigroups Book in PDF, ePub and Kindle
In this book, non-spectral methods are presented and discussed that have been developed over the last two decades for the investigation of asymptotic behavior of operator semigroups. This concerns in particular Markov semigroups in L1-spaces, motivated by applications to probability theory and dynamical systems. Related results, historical notes, exercises, and open problems accompany each chapter.
Author | : Tanja Eisner |
Publisher | : Birkhäuser |
Total Pages | : 208 |
Release | : 2019-10-01 |
Genre | : Mathematics |
ISBN | : 3034601956 |
Download Stability of Operators and Operator Semigroups Book in PDF, ePub and Kindle
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.
Author | : David Applebaum |
Publisher | : Cambridge University Press |
Total Pages | : 235 |
Release | : 2019-08-15 |
Genre | : Mathematics |
ISBN | : 1108623522 |
Download Semigroups of Linear Operators Book in PDF, ePub and Kindle
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.
Author | : Jerome A. Goldstein |
Publisher | : Courier Dover Publications |
Total Pages | : 320 |
Release | : 2017-05-17 |
Genre | : Mathematics |
ISBN | : 0486822222 |
Download Semigroups of Linear Operators and Applications Book in PDF, ePub and Kindle
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 | : Jacek Banasiak |
Publisher | : Springer |
Total Pages | : 493 |
Release | : 2014-11-07 |
Genre | : Mathematics |
ISBN | : 3319113224 |
Download Evolutionary Equations with Applications in Natural Sciences Book in PDF, ePub and Kindle
With the unifying theme of abstract evolutionary equations, both linear and nonlinear, in a complex environment, the book presents a multidisciplinary blend of topics, spanning the fields of theoretical and applied functional analysis, partial differential equations, probability theory and numerical analysis applied to various models coming from theoretical physics, biology, engineering and complexity theory. Truly unique features of the book are: the first simultaneous presentation of two complementary approaches to fragmentation and coagulation problems, by weak compactness methods and by using semigroup techniques, comprehensive exposition of probabilistic methods of analysis of long term dynamics of dynamical systems, semigroup analysis of biological problems and cutting edge pattern formation theory. The book will appeal to postgraduate students and researchers specializing in applications of mathematics to problems arising in natural sciences and engineering.
Author | : Klaus-Jochen Engel |
Publisher | : Springer Science & Business Media |
Total Pages | : 257 |
Release | : 2006-06-06 |
Genre | : Mathematics |
ISBN | : 0387313419 |
Download A Short Course on Operator Semigroups Book in PDF, ePub and Kindle
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 | : Vladimir Müller |
Publisher | : Springer Science & Business Media |
Total Pages | : 439 |
Release | : 2007-12-24 |
Genre | : Mathematics |
ISBN | : 3764382651 |
Download Spectral Theory of Linear Operators Book in PDF, ePub and Kindle
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.
Author | : Jack K. Hale |
Publisher | : American Mathematical Soc. |
Total Pages | : 210 |
Release | : 2010-01-04 |
Genre | : Mathematics |
ISBN | : 0821849344 |
Download Asymptotic Behavior of Dissipative Systems Book in PDF, ePub and Kindle
This monograph reports the advances that have been made in the area by the author and many other mathematicians; it is an important source of ideas for the researchers interested in the subject. --Zentralblatt MATH Although advanced, this book is a very good introduction to the subject, and the reading of the abstract part, which is elegant, is pleasant. ... this monograph will be of valuable interest for those who aim to learn in the very rapidly growing subject of infinite-dimensional dissipative dynamical systems. --Mathematical Reviews This book is directed at researchers in nonlinear ordinary and partial differential equations and at those who apply these topics to other fields of science. About one third of the book focuses on the existence and properties of the flow on the global attractor for a discrete or continuous dynamical system. The author presents a detailed discussion of abstract properties and examples of asymptotically smooth maps and semigroups. He also covers some of the continuity properties of the global attractor under perturbation, its capacity and Hausdorff dimension, and the stability of the flow on the global attractor under perturbation. The remainder of the book deals with particular equations occurring in applications and especially emphasizes delay equations, reaction-diffusion equations, and the damped wave equations. In each of the examples presented, the author shows how to verify the existence of a global attractor, and, for several examples, he discusses some properties of the flow on the global attractor.
Author | : András Bátkai |
Publisher | : Birkhäuser |
Total Pages | : 364 |
Release | : 2017-02-13 |
Genre | : Mathematics |
ISBN | : 3319428136 |
Download Positive Operator Semigroups Book in PDF, ePub and Kindle
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.