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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...

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