Topics in Operator Semigroups

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. (László Kérchy, 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 für 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)