Semigroups of Linear Operators (eBook)

With Applications to Analysis, Probability and Physics

David Applebaum (Autor)

eBook Download: EPUB

2019
Cambridge University Press (Verlag)
978-1-108-62352-0 (ISBN)

Infos

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.

Produkt-Details

• Erscheint lt. Verlag: 15.8.2019
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Mechanik
• ISBN-10: 1-108-62352-2 / 1108623522
• ISBN-13: 978-1-108-62352-0 / 9781108623520