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A characterization of evolution operators

Naoki Tanaka (2001)

Studia Mathematica

A class of evolution operators is introduced according to the device of Kato. An evolution operator introduced here provides a classical solution of the linear equation u'(t) = A(t)u(t) for t ∈ [0,T], in a general Banach space. The paper presents a necessary and sufficient condition for the existence and uniqueness of such an evolution operator.

A functional calculus description of real interpolation spaces for sectorial operators

Markus Haase (2005)

Studia Mathematica

For a holomorphic function ψ defined on a sector we give a condition implying the identity ( X , ( A α ) ) θ , p = x X | t - θ R e α ψ ( t A ) L p ( ( 0 , ) ; X ) where A is a sectorial operator on a Banach space X. This yields all common descriptions of the real interpolation spaces for sectorial operators and allows easy proofs of the moment inequalities and reiteration results for fractional powers.

A functional model for a family of operators induced by Laguerre operator

Hatamleh Ra'ed (2003)

Archivum Mathematicum

The paper generalizes the instruction, suggested by B. Sz.-Nagy and C. Foias, for operatorfunction induced by the Cauchy problem T t : t h ' ' ( t ) + ( 1 - t ) h ' ( t ) + A h ( t ) = 0 h ( 0 ) = h 0 ( t h ' ) ( 0 ) = h 1 A unitary dilatation for T t is constructed in the present paper. then a translational model for the family T t is presented using a model construction scheme, suggested by Zolotarev, V., [3]. Finally, we derive a discrete functional model of family T t and operator A applying the Laguerre transform f ( x ) 0 f ( x ) P n ( x ) e - x d x where P n ( x ) are Laguerre polynomials [6, 7]. We show that the Laguerre transform...

A general differentiation theorem for superadditive processes

Ryotaro Sato (2000)

Colloquium Mathematicae

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.

A local Landau type inequality for semigroup orbits

Gerd Herzog, Peer Christian Kunstmann (2014)

Studia Mathematica

Given a strongly continuous semigroup ( S ( t ) ) t 0 on a Banach space X with generator A and an element f ∈ D(A²) satisfying | | S ( t ) f | | e - ω t | | f | | and | | S ( t ) A ² f | | e - ω t | | A ² f | | for all t ≥ 0 and some ω > 0, we derive a Landau type inequality for ||Af|| in terms of ||f|| and ||A²f||. This inequality improves on the usual Landau inequality that holds in the case ω = 0.

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