Equisummability for Linear Operators in Banach Spaces

摘要

This reprint analyzes the behavior of analytic functions (e.g., resolvents semi-groups) of perturbed linear operators in Banach space. Specifically, we consider the effects of perturbations in certain natural parameters on strong continuity of such functions. In applications, these lead to results on the strong pointwise behavior of functions of elliptic operators. Examples for some second order elliptic operators will be given. An example for which these results are relevant involves the pointwise behavior of eigenfunction expansions. It is easier to study expansions in eigenfunctions of unperturbed operators (say - delta on a manifold), than of perturbed ones (say - delta + q(x)). Reprints. (KR)