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Generation of generators of holomorphic semigroups (journal paper)

Year: 
1993
Researcher(s): 
Christian Berg, Khristo Boyadzhiev and Ralph Delaubenfels
Institution: 
Ohio Northern University
Discipline: 
Mathematics

We construct a functional calculus, gg(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 {xs2016r(r + A)−1xs2016 ¦ r > 0} bounded. For such functions g, we show that –g(A) generates a bounded holomorphic strongly continuous semigroup of angle θ, whenever –A does.

We show that, for any Bernstein function f, − f(A) generates a bounded holomorphic strongly continuous semigroup of angle π/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.

From https://www.cambridge.org/core/journals/journal-of-the-australian-mathem...

Journal of the Australian Mathematical Society (Series A) / Volume 55 / Issue 02 / October 1993, pp 246-269