Consistent operator semigroups and their interpolation

TL;DR

This paper establishes that, under mild conditions, the generator of the interpolated C0-semigroup is the interpolation of the original generators, providing a new insight into the structure of operator semigroups.

Contribution

It proves a novel result linking the generators of interpolated C0-semigroups to the interpolation of their generators under mild regularity conditions.

Findings

The generator of the interpolated semigroup equals the interpolation of the original generators.

The result applies under mild regularity conditions.

Provides a theoretical foundation for analyzing semigroup interpolations.

Abstract

Under a mild regularity condition we prove that the generator of the interpolation of two C0-semigroups is the interpolation of the two generators.