On Joint Functional Calculus for Ritt Operators

A new functional calculus for noncommuting operators

In this paper we use the notion of slice monogenic functions [2] to define a new functional calculus for an n-tuple T of not necessarily commuting operators. This calculus is different from the one discussed in [5] and it allows the explicit construction of the eigenvalue equation for the n-tuple T based on a new notion of spectrum for T . Our functional calculus is consistent with the Riesz-Du...

Functional Calculus for Non-Commuting Operators

Functional calculus for tangentially elliptic operators on foliated manifolds ∗

3 Pseudodifferential functional calculus 7 3.1 Complex powers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3.2 Action in Sobolev spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 3.3 f(A) as pseudodifferential operators . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.4 The case of Finsler foliations . . . . . . . . . . . . ...

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...

Non commutative functional calculus: bounded operators

In this paper we develop a functional calculus for bounded operators defined on quaternionic Banach spaces. This calculus is based on the notion of slice-regularity, see [4], and the key tools are a new resolvent operator and a new eigenvalue problem. AMS Classification: 47A10, 47A60, 30G35.