On subordination of holomorphic semigroups

2014/08/06 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.1408.1417

Abstract

We prove that for any Bernstein function ψ the operator -ψ(A) generates a holomorphic C₀-semigroup (e^-tψ(A))_{t ≥ 0} on a Banach space, whenever -A does. This answers a question posed by Kishimoto and Robinson. Moreover, giving a positive answer to a question by Berg, Boyadzhiev and de Laubenfels, we show that (e^-tψ(A))_{t ≥ 0} is holomorphic in the holomorphy sector of (e^-tA)_{t ≥ 0}, and if (e^-tA)_{t ≥ 0} is sectorially bounded in this sector then (e^-tψ(A))_{t ≥ 0} has the same property. We also obtain new sufficient conditions on ψ in order that, for every Banach space X, the semigroup (e^-tψ(A))_{t≥ 0} on X is holomorphic whenever (e^-tA)_{t≥ 0} is a bounded C₀-semigroup on X. These conditions improve and generalize well-known results by Carasso-Kato and Fujita.

Related

• Generation of subordinated holomorphic semigroups via Yosida's theorem
• Criteria for analyticity of subordinate semigroups
• Criteria for Analyticity of Multidimensionally Subordinate Semigroups
• Resolvent representations for functions of sectorial operators
• Subordination for sequentially equicontinuous equibounded C₀-semigroups