This monograph is concerned with the interplay between the theory of operatorsemigroups 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--Katoapproximation 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. This monograph is suitable for graduate students and researchers interested in operator semigroups. 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 productformula, the Hille--Phillips perturbation theorem, and Stone’s representationof unitary semigroups Part II explores generalizations of spectral theory’s connection to operator semigroups Suitable for a graduate seminar on operator semigroups or for self study INDICE: Introduction.- Part I. General Theory. Basic theory. The semi-simplicity space. Analyticity. The semigroup as a function of its generator. Largeparameter. Boundary values.- Part II. Generalizations. Pre-semigroups. The semi-simplicity space. Families of unbounded symmetric operators. Dependence on parameters.- Notes and References. Bibliography.
- ISBN: 978-0-8176-4931-9
- Editorial: Birkhaüser
- Encuadernacion: Cartoné
- Páginas: 300
- Fecha Publicación: 01/12/2009
- Nº Volúmenes: 1
- Idioma: Inglés