General Theory.- Basic Theory.- The Semi-Simplicity Space for Groups.- Analyticity.- The Semigroup as a Function of its Generator.- Large Parameter.- Boundary Values.- Pre-Semigroups.- Integral Representations.- The Semi-Simplicity Space.- The Laplace#x2013;Stieltjes Space.- Families of Unbounded Symmetric Operators.- A Taste of Applications.- Analytic Families of Evolution Systems.- Similarity.
From the reviews: "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) "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)