Product formulas in functional calculi for sectorial operators

Sectorial Operators and Interpolation Theory

We present a survey of recent applications of interpolation ideas in the study of sectorial operators.

Semigroup Product Formulas and Addition of Unbounded Operators

H-functional Calculus and Models of Nagy-foiaş Type for Sectorial Operators

We prove that a sectorial operator admits an H∞functional calculus if and only if it has a functional model of NagyFoiaş type. Furthermore, we give a concrete formula for the characteristic function (in a generalized sense) of such an operator. More generally, this approach applies to any sectorial operator by passing to a different norm (the McIntosh square function norm). We also show that th...

Holomorphic Functional Calculi and Sums of Commuting Operators

Let S and T be commuting operators of type ! and type $ in a Banach space X. Then the pair has a joint holomorphic functional calculus in the sense that it is possible to deene operators f(S; T) in a consistent manner, when f is a suitable holomorphic function deened on a product of sectors. In particular, this gives a way to deene the sum S +T when ! +$ <. We show that this operator is always ...

Paley-Littlewood decomposition for sectorial operators and interpolation spaces

We prove Paley-Littlewood decompositions for the scales of fractional powers of 0-sectorial operators A on a Banach space which correspond to Triebel-Lizorkin spaces and the scale of Besov spaces if A is the classical Laplace operator on L(R). We use the H∞calculus, spectral multiplier theorems and generalized square functions on Banach spaces and apply our results to Laplace-type operators on ...