scholarly journals A Besov class functional calculus for bounded holomorphic semigroups

2005 ◽  
Vol 228 (2) ◽  
pp. 245-269 ◽  
Author(s):  
Pascale Vitse
Keyword(s):  
Functional Calculus ◽  
Besov Class ◽  
Holomorphic Semigroups ◽  
Bounded Holomorphic

scholarly journals A Besov algebra calculus for generators of operator semigroups and related norm-estimates

2019 ◽  
Author(s):  
Charles Batty ◽  
Alexander Gomilko ◽  
Yuri Tomilov
Keyword(s):  
Banach Spaces ◽  
Hilbert Spaces ◽  
Functional Calculus ◽  
The Other ◽  
Direct Approach ◽  
Operator Semigroups ◽  
Holomorphic Semigroups ◽  
Norm Estimates ◽  
Strict Extension ◽  
Bounded Holomorphic

Abstract We construct a new bounded functional calculus for the generators of bounded semigroups on Hilbert spaces and generators of bounded holomorphic semigroups on Banach spaces. The calculus is a natural (and strict) extension of the classical Hille–Phillips functional calculus, and it is compatible with the other well-known functional calculi. It satisfies the standard properties of functional calculi, provides a unified and direct approach to a number of norm-estimates in the literature, and allows improvements of some of them.

scholarly journals Generation of generators of holomorphic semigroups

1993 ◽  
Vol 55 (2) ◽  
pp. 246-269 ◽  
Author(s):  
Christian Berg ◽  
Khristo Boyadzhiev ◽  
Ralph Delaubenfels
Keyword(s):  
Functional Calculus ◽  
Continuous Semigroup ◽  
Monotone Function ◽  
Linear Operators ◽  
Bernstein Function ◽  
Strongly Continuous Semigroup ◽  
Resolvent Set ◽  
The Relationship ◽  
Bounded Holomorphic ◽  
Unbounded Linear Operators

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.

scholarly journals Functional Calculus for the Series of Semigroup Generators Via Transference

2019 ◽  
pp. 57-84
Author(s):  
Shawgy Hussein ◽  
Simon Joseph ◽  
Ahmed Sufyan ◽  
Murtada Amin ◽  
Ranya Tahire ◽  
...  
Keyword(s):  
Banach Space ◽  
Hilbert Space ◽  
Banach Spaces ◽  
Half Plane ◽  
Functional Calculus ◽  
Holomorphic Functions ◽  
Transference Principle ◽  
Semigroup Generators ◽  
Bounded Holomorphic ◽  
Semigroup Generator

In this paper, apply an established transference principle to obtain the boundedness of certain functional calculi for the sequence of semigroup generators. It is proved that if be the sequence generates 0- semigroups on a Hilbert space, then for each the sequence of operators has bounded calculus for the closed ideal of bounded holomorphic functions on right half–plane. The bounded of this calculus grows at most logarithmically as. As a consequence decay at ∞. Then showed that each sequence of semigroup generator has a so-called (strong) m-bounded calculus for all m∈ℕ, and that this property characterizes the sequence of semigroup generators. Similar results are obtained if the underlying Banach space is a UMD space. Upon restriction to so-called semigroups, the Hilbert space results actually hold in general Banach spaces.

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