The complex inversion formula in UMD spaces for families of bounded operators

Abstract

In this article, we prove that in UMD Banach spaces the complex inversion formula of the Laplace transform is valid, in the strong sense, for wide classes of families of bounded linear operators. Our approach allows us to recover (in a unified way) known results about C ₀-semigroups, cosine functions and resolvent families as well as to prove new results for k-convoluted semigroups and integrated semigroups, among others.

Keywords:

• UMD spaces
• complex inversion of Laplace transform
• k-convoluted semigroups

AMS Subject Classifications::

• 34G10
• 43A50
• 44A10

Acknowledgement

The first author is partially supported by FONDECYT grant number 1100485.