14 citations · 37 across the 11 of their papers we have counts for
15 papers
Universality property of the -functional calculus, noncommuting matrix variables and Clifford operators
Fabrizio Colombo, Jonathan Gantner, David P. Kimsey +1
The spectral theory on the -spectrum was born out of the need to give quaternionic quantum mechanics (formulated by Birkhoff and von Neumann) a precise mathematical foundation.…
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…
Fractional powers of vector operators and fractional Fourier's law in a Hilbert space
Fabrizio Colombo, Jonathan Gantner
In this paper we give a concrete application of the spectral theory based on the notion of -spectrum to fractional diffusion process. Precisely, we consider the Fourier law for…
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…
On the Equivalence of Complex and Quaternionic Quantum Mechanics
Jonathan Gantner
Due to the existence of incompatible observables, the propositional calculus of a quantum system does not form a Boolean algebra but an orthomodular lattice. Such lattice can be re…