Automatic extensions of functional calculi

Ralph deLaubenfels

Displaying similar documents to “Automatic extensions of functional calculi”

Functional calculi, regularized semigroups and integrated semigroups

Ralph deLaubenfels, Mustapha Jazar (1999)

Studia Mathematica

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We characterize closed linear operators A, on a Banach space, for which the corresponding abstract Cauchy problem has a unique polynomially bounded solution for all initial data in the domain of $A^{n}$ , for some nonnegative integer n, in terms of functional calculi, regularized semigroups, integrated semigroups and the growth of the resolvent in the right half-plane. We construct a semigroup analogue of a spectral distribution for such operators, and an extended functional calculus: When...

Regularized functional calculi, semigroups, and cosine functions for pseudodifferential operators.

deLaubenfels, Ralph, Lei, Yansong (1997)

Abstract and Applied Analysis

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Spectral projections, semigroups of operators, and the Laplace transform

Ralph deLaubenfels (1997)

Banach Center Publications

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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. ...

Integral formulae for special cases of Taylor's functional calculus

D. Albrecht (1993)

Studia Mathematica

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In this paper integral formulae, based on Taylor's functional calculus for several operators, are found. Special cases of these formulae include those of Vasilescu and Janas, and an integral formula for commuting operators with real spectra.

A general differentiation theorem for superadditive processes

Ryotaro Sato (2000)

Colloquium Mathematicae

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Let L be a Banach lattice of real-valued measurable functions on a σ-finite measure space and T= $T_{t}$ : t < 0 be a strongly continuous semigroup of positive linear operators on the Banach lattice L. Under some suitable norm conditions on L we prove a general differentiation theorem for superadditive processes in L with respect to the semigroup T.

The monogenic functional calculus

Brian Jefferies, Alan McIntosh, James Picton-Warlow (1999)

Studia Mathematica

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A study is made of a symmetric functional calculus for a system of bounded linear operators acting on a Banach space. Finite real linear combinations of the operators have real spectra, but the operators do not necessarily commute with each other. Analytic functions of the operators are formed by using functions taking their values in a Clifford algebra.

A constructive proof of the composition rule for Taylor's functional calculus

Mats Andersson, Sebastian Sandberg (2000)

Studia Mathematica

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We give a new constructive proof of the composition rule for Taylor's functional calculus for commuting operators on a Banach space.

Integral representation of functions on sectors, functional calculus and norm estimates.

Khristo N. Boyadzhiev (2002)

Collectanea Mathematica

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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 ${e^{- s A}}_{s \leq 0}$ 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 ${e^{- s A}}_{s \geq 0}$ and ∃ M < ∞ such that $∥ H_{n} (s) ∥ \equiv ∥ (\sum_{k = 0}^{n} (s^{k} A^{k}) / k!) e^{- s A} ∥ \leq M$ , ∀s > 0, n ∈ ℕ ∪ 0. (4) -A generates a strongly continuous holomorphic semigroup ${e^{- z A}}_{R e (z) > 0}$ that is O(|z|)...