This monograph is concerned with the interplay between the theory of operator semigroups and spectral theory. The basics on operator semigroups are concisely covered in this self-contained text. Part I deals with the Hille--Yosida and Lumer--Phillips characterizations of semigroup generators, the Trotter--Kato approximation theorem, Kato's unified treatment of the exponential formula and the Trotter product formula, the Hille--Phillips perturbation theorem, and Stone's representation of unitary semigroups. Part II explores generalizations of spectral theory's connection to operator semigroups.
Title: Topics in Operator Semigroups: 281 (Progress in Mathematics)
Author: Kantorovitz, Shmuel
ISBN: 9780817649319
Binding:
Publisher: Birkhauser Boston Inc
Publication Date: 2009-12-01
Number of Pages: 266
Weight: 0.5445 kg
From the book reviews:
This monograph is suitable for second-year graduate students, but it can be recommended also to any researcher interested in operator semigroups. (Laszlo Kerchy, Acta Scientiarum Mathematicarum (Szeged), Vol. 78 (1-2), 2012)
The present graduate level text expands the previous lecture notes from the same author, Semigroups of operators and spectral theory ... . It begins with a succinct introduction to operator semigroups covering classical topics such as generators, the Hille-Yosida theorem, dissipative operators and the Lumer-Phillips theorem, the Trotter convergence theorem, exponential formulas, perturbation theory, Stone's theorem, and analytic semigroups. ... The text is also intended for second-year graduate students ... . it will be a valuable source for researchers working in this area. (G. Teschl, Monatshefte fur Mathematik, Vol. 162 (4), April, 2011)
This book is based on the author's lecture notes ... in which the more advanced parts concentrated on spectral representations. ... There is also a presentation of a well-known stability theorem for semigroups under countable spectral conditions. ... The increased variety of topics covered will make the book more useful ... . Other advantages are the inclusion of an index and some exercises, considerable extensions of the bibliography and the list of contents, and more attractive typesetting. (C. J. K. Batty, Mathematical Reviews, Issue 2010 k)
