Positive Operator Semigroups
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One parameter Semigroups of Positive Operators
Author | : Wolfgang Arendt,Rainer Nagel,Annette Grabosch,Günther Greiner,Ulrich Groh,Heinrich P. Lotz,Ulrich Moustakas,Frank Neubrander,Ulf Schlotterbeck |
Publsiher | : Springer |
Total Pages | : 468 |
Release | : 2006-11-14 |
Genre | : Mathematics |
ISBN | : 9783540397915 |
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Positive Semigroups of Operators and Applications
Author | : O. Bratteli,P.E.T. Jørgensen |
Publsiher | : Springer Science & Business Media |
Total Pages | : 200 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 9789400964846 |
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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
Positive Operator Semigroups
Author | : András Bátkai,Marjeta Kramar Fijavž,Abdelaziz Rhandi |
Publsiher | : Birkhäuser |
Total Pages | : 364 |
Release | : 2017-02-13 |
Genre | : Mathematics |
ISBN | : 9783319428130 |
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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.
Positive Operator Semigroups
Author | : András Bátkai,Marjeta Kramar Fijavž,Abdelaziz Rhandi |
Publsiher | : Unknown |
Total Pages | : 135 |
Release | : 2017 |
Genre | : Algebra |
ISBN | : 3319428128 |
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.
A Short Course on Operator Semigroups
Author | : Klaus-Jochen Engel,Rainer Nagel |
Publsiher | : Springer Science & Business Media |
Total Pages | : 257 |
Release | : 2006-06-06 |
Genre | : Mathematics |
ISBN | : 9780387313412 |
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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.
Positive Operators and Semigroups on Banach Lattices
Author | : C.B. Huijsmans,Wilhelm A.J. Luxemburg |
Publsiher | : Springer Science & Business Media |
Total Pages | : 151 |
Release | : 2013-03-09 |
Genre | : Mathematics |
ISBN | : 9789401727211 |
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During the last twenty-five years, the development of the theory of Banach lattices has stimulated new directions of research in the theory of positive operators and the theory of semigroups of positive operators. In particular, the recent investigations in the structure of the lattice ordered (Banach) algebra of the order bounded operators of a Banach lattice have led to many important results in the spectral theory of positive operators. The contributions contained in this volume were presented as lectures at a conference organized by the Caribbean Mathematics Foundation, and provide an overview of the present state of development of various areas of the theory of positive operators and their spectral properties. This book will be of interest to analysts whose work involves positive matrices and positive operators.
Semigroups of Linear Operators
Author | : David Applebaum |
Publsiher | : Cambridge University Press |
Total Pages | : 235 |
Release | : 2019-08-15 |
Genre | : Mathematics |
ISBN | : 9781108483094 |
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Provides a graduate-level introduction to the theory of semigroups of operators.
The Asymptotic Behaviour of Semigroups of Linear Operators
Author | : Jan van Neerven |
Publsiher | : Birkhäuser |
Total Pages | : 247 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 9783034892063 |
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.