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An introduction to hyperholomorphic spectral theories and fractional powers of vector operators
Fabrizio Colombo, Jonathan Gantner, Stefano Pinton
The aim of this paper is to give an overview of the spectral theories associated with the notions of holomorphicity in dimension greater than one. A first natural extension is the…
An Application of the -Functional Calculus to Fractional Diffusion Processes
Fabrizio Colombo, Jonathan Gantner
In this paper we show how the spectral theory based on the notion of -spectrum allows us to study new classes of fractional diffusion and of fractional evolution processes. We p…
Operator Theory on One-Sided Quaternionic Linear Spaces: Intrinsic S-Functional Calculus and Spectral Operators
Jonathan Gantner
Two themes drive this article: identifying the structure necessary to formulate quaternionic operator theory and revealing the relation between complex and quaternionic operator th…
A direct approach to the S-functional calculus for closed operators
Jonathan Gantner
The -functional calculus for slice hyperholomorphic functions generalizes the Riesz-Dunford-functional calculus for holomorphic functions to quaternionic linear operators and to…
Functions of the infinitesimal generator of a strongly continuous quaternionic group
Daniel Alpay, Fabrizio Colombo, Jonathan Gantner +1
The analogue of the Riesz-Dunford functional calculus has been introduced and studied recently as well as the theory of semigroups and groups of linear quaternionic operators. In t…