Functional calculus for generators of analytic semigroups of operators

Abstract

We construct a functional calculus for generators of one-parameter bounded analytic semigroups of operators on a Banach space. The calculus symbol class consist of the Laplace image of the convolution algebra $\cal S'_+$ of tempered distributions with supports in $[0, \infty)$. Domain of constructed calculus is dense in the Banach space.