Distances between elements of a semigroup and estimates for derivatives

Autor:	Jonathan R. Partington, Isabelle Chalendar, Zohra Bendouad, Jean Esterle
Rok vydání:	2010
Předmět:	Discrete mathematics Analytic semigroup Pure mathematics Mathematics::Operator Algebras Semigroup Applied Mathematics General Mathematics Banach space Cancellative semigroup Norm (mathematics) Bounded function Bicyclic semigroup Real line Mathematics
Zdroj:	Acta Mathematica Sinica, English Series. 26:2239-2254
ISSN:	1439-7617 1439-8516
DOI:	10.1007/s10114-010-8569-6
Popis:	This paper is concerned first with the behaviour of differences T(t)-T(s) near the origin, where (T(t)) is a semigroup of operators on a Banach space, defined either on the positive real line or a sector in the right half-plane (in which case it is assumed analytic). For the non-quasinilpotent case extensions of results in the published literature are provided, with best possible constants; in the case of quasinilpotent semigroups on the half-plane, it is shown that, in general, differences such as T(t)-T(2t) have norm approaching 2 near the origin. The techniques given enable one to derive estimates of other functions of the generator of the semigroup; in particular, conditions are given on the derivatives near the origin to guarantee that the semigroup generates a unital algebra and has bounded generator.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::5f69e5944f0ad8511d5b32881a6cbfd7 https://doi.org/10.1007/s10114-010-8569-6 Zobrazit plný text záznamu Plný text ve formátu PDF