J Austral Math Soc Ser A 55 pp246--269, 1993.

Generation of Generators of Holomorphic Semigroups

Christian Berg, Khristo Boyadzhiev and Ralph Delaubenfels

Abstract

We construct a functional calculus, g ® g(A), for functions, g, that are the sum of a Stieltjes function and a nonnegative operator monotone function, and unbounded linear operators, A, whose resolvent set contains (-¥, 0), with {||r(r + A)^-1|| | r > 0} bounded. For such functions g, we show that -g(A) generates a bounded holomorphic strongly continuous semigroups of angle q, whenever -A does. We show that, for any Bernstein function f, -f(A) generates a bounded holomorphic strongly continuous semigroup of angle p/2, whenever -A does. We also prove some new results about the Bochner-Phillips functional calculus. We discuss the relationship between fractional powers and our construction.

1991 AMS Subject Classification: 47A60, 47B44, 47D05

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Authors

Christian Berg

Matematisk Institut, Universitetsparken 5, DK-2100, Kobenhavn ø, Denmark.

Khristo Boyadzhiev

Ohio Northern University, Ada, Ohio 45810, USA.

Ralph Delaubenfels

Ohio University, Athens, Ohio 45701, USA.