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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 notion of analytic generator for groups of unbounded operators

José E. Galé (2005)

Banach Center Publications

We introduce a notion of analytic generator for groups of unbounded operators, on Banach modules, arising from Esterle’s quasimultiplier theory. Characterizations of analytic generators are given in terms of the existence of certain functional calculi. This extends recent results about C₀ groups of bounded operators. The theory is applicable to sectorial operators, representations of H , and integrated groups.

A way of estimating the convergence rate of the Fourier method for PDE of hyperbolic type

Evgenii Pustylnik (2001)

Czechoslovak Mathematical Journal

The Fourier expansion in eigenfunctions of a positive operator is studied with the help of abstract functions of this operator. The rate of convergence is estimated in terms of its eigenvalues, especially for uniform and absolute convergence. Some particular results are obtained for elliptic operators and hyperbolic equations.

An M q ( ) -functional calculus for power-bounded operators on certain UMD spaces

Earl Berkson, T. A. Gillespie (2005)

Studia Mathematica

For 1 ≤ q < ∞, let q ( ) denote the Banach algebra consisting of the bounded complex-valued functions on the unit circle having uniformly bounded q-variation on the dyadic arcs. We describe a broad class ℐ of UMD spaces such that whenever X ∈ ℐ, the sequence space ℓ²(ℤ,X) admits the classes q ( ) as Fourier multipliers, for an appropriate range of values of q > 1 (the range of q depending on X). This multiplier result expands the vector-valued Marcinkiewicz Multiplier Theorem in the direction q >...

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