## Differential and Integral Equations

### Regularized semigroups, existence families and the abstract Cauchy problem

#### Abstract

For an arbitrary bounded linear operator $C$, on a Banach space, and a closable linear operator $A$, we introduce a $C$-regularized semigroup for $A$. We present equivalences between $A$ having a $C$-regularized semigroup, the corresponding abstract Cauchy problem, well-posedness on a continuously embedded subspace, and (for exponentially bounded $C$-regularized semigroups) the Laplace transform.

#### Article information

Source
Differential Integral Equations, Volume 8, Number 6 (1995), 1477-1496.

Dates
First available in Project Euclid: 15 May 2013