Criteria for analyticity of subordinate semigroups

Миротин, А. Р.

doi:10.1007/s00233-008-9090-4

Cited by 16 publications

(15 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…This will be derived as a simple consequence of the following operator norm estimate for ψ(A)g(A) where ψ ∈ BF and g ∈ BCM. In a different context, a related estimate was obtained in [16,Theorem 1].…”

Section: Resultsmentioning

confidence: 98%

Generation of Subordinated Holomorphic Semigroups via Yosida’s Theorem

Gomilko

Tomilov

2015

Operator Semigroups Meet Complex Analysis, Harmonic Analysis and Mathematical Physics

View full text Add to dashboard Cite

Abstract. 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.

show abstract

Section: Resultsmentioning

confidence: 98%

Generation of Subordinated Holomorphic Semigroups via Yosida’s Theorem

Gomilko

Tomilov

2015

Operator Semigroups Meet Complex Analysis, Harmonic Analysis and Mathematical Physics

View full text Add to dashboard Cite

show abstract

“…Certain sufficient conditions for a Bernstein function to be Carasso-Kato were obtained in [6,9,22,23,30]. Interesting applications of Carasso-Kato functions can be found in [5,10,19].…”

Section: Introductionmentioning

confidence: 96%

On subordination of holomorphic semigroups

Gomilko

Tomilov

2015

Advances in Mathematics

View full text Add to dashboard Cite

We prove that for any Bernstein function ψ the operator −ψ(A) generates a bounded holomorphic C 0 -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 C 0 -semigroup on X. These conditions improve and generalize well-known results by Carasso-Kato and Fujita.

show abstract

“…As was mentioned in [17], the one-dimensional Bochner-Phillips functional calculus is a substantial part of the theory of operator semigroups and finds important applications in the theory of random processes (see, e.g., [19], [20]). The foundations of multidimensional calculus were laid by the author in [21], [22], [23], [24], [25].…”

Section: Introductionmentioning

confidence: 99%

“…A lot of examples of Bernstein function of one variable one can found in [34] (see also [20], [26]). Throughout the paper, T A 1 , .…”

Section: Introductionmentioning

confidence: 99%

Bernstein functions of several semigroup generators on Banach spaces under bounded perturbations, II

Миротин¹

2018

Operators and Matrices

Self Cite

View full text Add to dashboard Cite

The paper deals with multidimensional Bochner-Phillips functional calculus. In the previous paper by the author bounded perturbations of Bernstein functions of several commuting semigroup generators on Banach spaces where considered, conditions for Lipschitzness and estimates for the norm of commutators of such functions where proved. Also in the one-dimensional case the Frechet differentiability of Bernstein functions of semigroup generators on Banach spaces where proved and a generalization of Livschits-Kreȋn trace formula derived. The aim of the present paper is to prove the Frechet differentiability of operator Bernstein functions and the Livschits-Kreȋn trace formula in the multidimensional setting.

show abstract

Criteria for analyticity of subordinate semigroups

Cited by 16 publications

References 19 publications

Generation of Subordinated Holomorphic Semigroups via Yosida’s Theorem

Generation of Subordinated Holomorphic Semigroups via Yosida’s Theorem

On subordination of holomorphic semigroups

Bernstein functions of several semigroup generators on Banach spaces under bounded perturbations, II

Contact Info

Product

Resources

About