Summary: For a large subclass of Bernstein functions \(f\) we prove a new integral representation formula for the generator \(A^f\) of a subordinate \((C_0)\)-semigroup on a Banach space. We show that \(A^f=-f(-A)\) in the sense of Dunford’s operational calculus. If \(A\), \(B\) are two selfadjoint generators, order relations for the associated quadratic forms are preserved, and if \(D(A)=D(B)\) we then have \(D(A^f)=D(B^f)\). As an application, we can describe the domain of certain pseudo-differential operators generating Feller semigroups.
For the entire collection see [Zbl 0844.00023].