Operator calculus on the class of Sato's hyperfunctions - Patra M.I.; Sharyn S.V. (Karpatsʹkì Matematičnì Publìkacìï, 2013)
We construct a functional calculus for generators of analytic semigroupsof operators on a Banach space. The symbol class of the calculusconsists of hyperfunctions with a compact support in $[0, infty)$. Domain of constructedcalculus isdense in the Banach space.