Semigroups of Linear Operators - With Applications to Analysis, Probability and Physics

Provides a graduate-level introduction to the theory of semigroups of operators.

List of contents

Introduction; 1. Semigroups and generators; 2. The generation of semigroups; 3. Convolution semigroups of measures; 4. Self adjoint semigroups and unitary groups; 5. Compact and trace class semigroups; 6. Perturbation theory; 7. Markov and Feller semigroups; 8. Semigroups and dynamics; 9. Varopoulos semigroups; Notes and further reading; Appendices: A. The space C0(Rd); B. The Fourier transform; C. Sobolev spaces; D. Probability measures and Kolmogorov's theorem on construction of stochastic processes; E. Absolute continuity, conditional expectation and martingales; F. Stochastic integration and Itô's formula; G. Measures on locally compact spaces: some brief remarks; References; Index.

About the author

David Applebaum is Professor of Mathematics at the University of Sheffield. His specialist research area is stochastic analysis, with particular emphasis on analytic and probabilistic aspects of processes with jumps on Lie groups, symmetric spaces and manifolds.

Summary

The theory of semigroups of operators is a topic with great intellectual beauty and wide-ranging applications. This graduate-level introduction presents the essential elements of the theory, introducing the key notions and establishing the central theorems. A mixture of applications are included and further development directions are indicated.

Product details

• Authors: David Applebaum, David (University of Sheffield) Applebaum, Applebaum David
• Publisher: Cambridge University Press ELT
• Languages: English
• Product format: Paperback / Softback
• Released: 31.08.2019
• EAN: 9781108716376
• ISBN: 978-1-108-71637-6
• No. of pages: 232
• Series: London Mathematical Society Student Texts; London Mathematical Society St
• Subjects: Natural sciences, medicine, IT, technology > Physics, astronomy > Mechanics, acoustics; SCIENCE / Physics / Mathematical & Computational, SCIENCE / Mechanics / Dynamics, Mathematical physics, Stochastics, Dynamics & statics, SCIENCE / Mechanics / Statics, Dynamics and statics