TY  - BOOK
AU  - Applebaum,David
TI  - Semigroups of linear operators: with applications to analysis, probability and physics 
T2  - London Mathematical Society student texts
SN  - 9781108672641 (ebook)
AV  - QA329.2 .A687 2019
U1  - 515/.7246 23
PY  - 2019///
CY  - Cambridge
PB  - Cambridge University Press
KW  - Linear operators
KW  - Textbooks
KW  - Operator theory
KW  - Semigroups
KW  - Group theory
N1  - Title from publisher's bibliographic system (viewed on 26 Jul 2019)
N2  - 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
UR  - https://doi.org/10.1017/9781108672641
ER  -