Generation of generators of holomorphic semigroups

Journal of the Australian Mathematical Society

Christian Berg¹ 

[1] Khristo Boyadzhiev

关键词: 47 A 60;    47 B 44;    47 D 05;   

DOI  :  10.1017/S1446788700032067

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

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 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.

【 授权许可】

Unknown