Generation of generators of holomorphic semigroups
1993 ◽
Vol 55
(2)
◽
pp. 246-269
◽
Keyword(s):
AbstractWe 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.
1995 ◽
Vol 47
(4)
◽
pp. 744-785
◽
1964 ◽
Vol 60
(1)
◽
pp. 45-49
◽
1990 ◽
Vol 32
(3)
◽
pp. 273-276
◽
2010 ◽
Vol 70
(3)
◽
pp. 363-378
◽
1995 ◽
Vol 1
(3)
◽
pp. 179-191
◽
1975 ◽
Vol 12
(1)
◽
pp. 23-25
◽
Keyword(s):
2008 ◽
pp. 337-372