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Distances between Elements of a Semigroup and Estimates for Derivatives Zohra BENDOUAD Isabelle CHALENDAR Jean ESTERLE Jonathan R.PARTINGTON Abstract 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
Distances between Elements of a Semigroup and Estimates for Derivatives Zohra BENDOUAD Isabelle CHALENDAR Jean ESTERLE Jonathan R. PARTINGTON Abstract This paper is concerned first with the behavior 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