Operator calculus on the class of Sato’s hyperfunctions

Abstract

We construct a functional calculus for generators of analytic semigroups of operators on a Banach space. The symbol class of the calculus consists of hyperfunctions with a compact support in $[0,\infty)$. Domain of constructed calculus is dense in the Banach space.

Keywords

• functional calculus
• analytic semigroups of operators
• hyperfunctions