Convergence of One-parameter Operator Semigroups

Convergence of One-parameter Operator Semigroups
Author: Adam Bobrowski
Publisher: Cambridge University Press
Total Pages: 453
Release: 2016-07-14
Genre: Mathematics
ISBN: 1107137438

Presents the classical theory of convergence of semigroups and looks at how it applies to real-world phenomena.

One-Parameter Semigroups for Linear Evolution Equations

One-Parameter Semigroups for Linear Evolution Equations
Author: Klaus-Jochen Engel
Publisher: Springer Science & Business Media
Total Pages: 609
Release: 2006-04-06
Genre: Mathematics
ISBN: 0387226427

This book explores the theory of strongly continuous one-parameter semigroups of linear operators. A special feature of the text is an unusually wide range of applications such as to ordinary and partial differential operators, to delay and Volterra equations, and to control theory. Also, the book places an emphasis on philosophical motivation and the historical background.

Non-spectral Asymptotic Analysis of One-Parameter Operator Semigroups

Non-spectral Asymptotic Analysis of One-Parameter Operator Semigroups
Author: Eduard Yu. Emel'yanov
Publisher: Springer Science & Business Media
Total Pages: 181
Release: 2007-02-17
Genre: Mathematics
ISBN: 3764381140

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.

A Short Course on Operator Semigroups

A Short Course on Operator Semigroups
Author: Klaus-Jochen Engel
Publisher: Springer Science & Business Media
Total Pages: 257
Release: 2006-06-06
Genre: Mathematics
ISBN: 0387313419

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.

Positivity and its Applications

Positivity and its Applications
Author: Eder Kikianty
Publisher: Springer Nature
Total Pages: 321
Release: 2021-07-22
Genre: Mathematics
ISBN: 3030709744

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.

Stability of Operators and Operator Semigroups

Stability of Operators and Operator Semigroups
Author: Tanja Eisner
Publisher: Birkhäuser
Total Pages: 208
Release: 2019-10-01
Genre: Mathematics
ISBN: 3034601956

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.

Gibbs Semigroups

Gibbs Semigroups
Author: Valentin A. Zagrebnov
Publisher: Springer Nature
Total Pages: 328
Release: 2019-11-17
Genre: Mathematics
ISBN: 3030188779

This book focuses on the theory of the Gibbs semigroups, which originated in the 1970s and was motivated by the study of strongly continuous operator semigroups with values in the trace-class ideal. The book offers an up-to-date, exhaustive overview of the advances achieved in this theory after half a century of development. It begins with a tutorial introduction to the necessary background material, before presenting the Gibbs semigroups and then providing detailed and systematic information on the Trotter-Kato product formulae in the trace-norm topology. In addition to reviewing the state-of-art concerning the Trotter-Kato product formulae, the book extends the scope of exposition from the trace-class ideal to other ideals. Here, special attention is paid to results on semigroups in symmetrically normed ideals and in the Dixmier ideal. By examining the progress made in Gibbs semigroup theory and in extensions of the Trotter-Kato product formulae to symmetrically normed and Dixmier ideals, the book shares timely and valuable insights for readers interested in pursuing these subjects further. As such, it will appeal to researchers, undergraduate and graduate students in mathematics and mathematical physics.