2014/10/06 by Gomilko, Alexander, Tomilov, Yuri
#26A48 #47D03 #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Primary 47A60 #Probability (math.PR) #Secondary 46N30
paper · doi:10.48550/arxiv.1410.1505
Using functional calculi theory, we obtain several estimates for ‖ψ(A)g(A)‖, where ψ is a Bernstein function, g is a bounded completely monotone function and -A is the generator of a holomorphic C0-semigroup on a Banach space, bounded on [0,∞). Such estimates are of value, in particular, in approximation theory of operator semigroups. As a corollary, we obtain a new proof of the fact that -ψ(A) generates a holomorphic semigroup whenever -A does, established recently in [8] by a different approach.