Displaying similar documents to “Functional calculi, regularized semigroups and integrated semigroups”

On α-times integrated C-semigroups and the abstract Cauchy problem

Chung-Cheng Kuo, Sen-Yen Shaw (2000)

Studia Mathematica

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This paper is concerned with α-times integrated C-semigroups for α > 0 and the associated abstract Cauchy problem: u ' ( t ) = A u ( t ) + t α - 1 Γ ( α ) x , t >0; u(0) = 0. We first investigate basic properties of an α-times integrated C-semigroup which may not be exponentially bounded. We then characterize the generator A of an exponentially bounded α-times integrated C-semigroup, either in terms of its Laplace transforms or in terms of existence of a unique solution of the above abstract Cauchy problem for every x...

On analytic semigroups and cosine functions in Banach spaces

V. Keyantuo, P. Vieten (1998)

Studia Mathematica

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If A generates a bounded cosine function on a Banach space X then the negative square root B of A generates a holomorphic semigroup, and this semigroup is the conjugate potential transform of the cosine function. This connection is studied in detail, and it is used for a characterization of cosine function generators in terms of growth conditions on the semigroup generated by B. The characterization relies on new results on the inversion of the vector-valued conjugate potential transform. ...

Automatic extensions of functional calculi

Ralph deLaubenfels (1995)

Studia Mathematica

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Given a Banach algebra ℱ of complex-valued functions and a closed, linear (possibly unbounded) densely defined operator A, on a Banach space, with an ℱ functional calculus we present two ways of extending this functional calculus to a much larger class of functions with little or no growth conditions. We apply this to spectral operators of scalar type, generators of bounded strongly continuous groups and operators whose resolvent set contains a half-line. For f in this larger class,...

On a class of Markov type semigroups in spaces of uniformly continuous and bounded functions

Enrico Priola (1999)

Studia Mathematica

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We study a new class of Markov type semigroups (not strongly continuous in general) in the space of all real, uniformly continuous and bounded functions on a separable metric space E. Our results allow us to characterize the generators of Markov transition semigroups in infinite dimensions such as the heat and the Ornstein-Uhlenbeck semigroups.

Unbounded well-bounded operators, strongly continuous semigroups and the Laplace transform

Ralph deLaubenfels (1992)

Studia Mathematica

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Suppose A is a (possibly unbounded) linear operator on a Banach space. We show that the following are equivalent. (1) A is well-bounded on [0,∞). (2) -A generates a strongly continuous semigroup e - s A s ≤ 0 such that ( 1 / s 2 ) e - s A s > 0 is the Laplace transform of a Lipschitz continuous family of operators that vanishes at 0. (3) -A generates a strongly continuous differentiable semigroup e - s A s ≥ 0 and ∃ M < ∞ such that ∥ H n ( s ) ∥ ≡ ∥ ( ∑ k = 0 n ( s k A k ) / k ! ) e - s A ∥ ≤ M , ∀s > 0, n ∈ ℕ ∪ 0. (4) -A generates a strongly continuous holomorphic semigroup e - z A R e ( z ) > 0 that is O(|z|)...