Distance between elements of a semigroup and estimates for derivatives
Langue
en
Article de revue
Ce document a été publié dans
Acta Mathematica Sinica English Series. 2010-12, vol. 26, n° 11, p. 2239-2254
Springer Verlag
Résumé en anglais
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 ...Lire la suite >
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.< Réduire
Mots clés en anglais
Semigroup of operators
analytic semigroup
Banach algebras
non-quasinilpotent
quasi- nilpotent
Origine
Importé de halUnités de recherche