Semigroups of Linear Operators: With Applications to Analysis, Probability and Physics (Hardcover) (ISBN-13: 9781108483094)

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: David Applebaum
ISBN-10: 1108483097
ISBN-13: 9781108483094
Publisher: Cambridge University Press
Language: English
Published: 08/15/2019
Pages: 232
Format: Hardcover
Weight: 1.00lbs
Size: 9.22h x 6.43w x 0.69d

Review Citation(s):
Choice 04/01/2020