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math.FA2018
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…
math.SP2018
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…
math.SP2018
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…