Bernstein Functions

Generation of Subordinated Holomorphic Semigroups via Yosida’s Theorem

“…As proved in [19], if −A is the generator of a bounded C 0 -semigroup on X and ψ ∈ BF, then If ψ(τ ) = τ α , α ∈ (0, 1), then (3.15) reduces to the classical moment inequality for fractional powers of A. Using our technique, we obtain the following corollary of (3.15).…”

“…We finish with relating our estimates to the following generalization of the moment inequality for generators of bounded C 0 -semigroups given in [19,Corollary 12.18]. As proved in [19], if −A is the generator of a bounded C 0 -semigroup on X and ψ ∈ BF, then If ψ(τ ) = τ α , α ∈ (0, 1), then (3.15) reduces to the classical moment inequality for fractional powers of A.…”

“…The next classical characterization of Bernstein functions goes back to Bochner and can be found e.g. in [19,Theorem 5.2]. for all t ≥ 0.…”

“…Function theory. Let us recall some basic facts on completely monotone and Bersntein functions from [19] relevant for the following. …”

Complete Monotonicity of a Difference Between the Exponential and Trigamma Functions and Properties Related to a Modified Bessel Function

“…Recall from [8,Chapter XIII], [14,Chapter 1] and [15, Chapter IV] that a function f is said to be completely monotonic on an interval I if f has derivatives of all orders on I and satisfies (−1) n f (n) (x) ≥ 0 (1.1) for x ∈ I and n ∈ {0} ∪ N. The exponential function e 1/z for z ∈ C with z = 0 can be expanded into the Laurent series for z ∈ C \ {0, −1, −2, . .…”