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

ISBN-13: 9781108716376 / Angielski / Miękka / 2019 / 232 str.

David Applebaum

Opis

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.

Recenzje

'This excellent book, supplementing the known texts on operator semigroups, stems from the author's lectures for students with basic knowledge of functional analysis and measure theory … the book totally meets the goals of the LMS Student Texts series and is highly recommended to the University community.' Andrey V. Bulinski, zbMATH

Spis treści

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.