H∞functional calculus for sectorial and bisectorial operators

Sectorial Operators and Interpolation Theory

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

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 ...

Generation of Equicontinuous Semigroups by Hermitian and Sectorial Operators. I

On certain fractional calculus operators involving generalized Mittag-Leffler function

The object of this paper is to establish certain generalized fractional integration and differentiation involving generalized Mittag-Leffler function defined by Salim and Faraj [25]. The considered generalized fractional calculus operators contain the Appell's function $F_3$ [2, p.224] as kernel and are introduced by Saigo and Maeda [23]. The Marichev-Saigo-Maeda fractional calculus operators a...