108 citations · 443 across the 80 of their papers we have counts for
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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…
Poly slice monogenic functions, Cauchy formulas and the PS-functional calculus
Daniel Alpay, Fabrizio Colombo, Kamal Diki +1
Since 2006 the theory of slice hyperholomorphic functions and the related spectral theory on the S-spectrum have had a very fast development. This new spectral theory based on the…
Infinite order differential operators acting on entire hyperholomorphic functions
Daniel Alpay, Fabrizio Colombo, Stefano Pinton +2
Infinite order differential operators appear in different fields of Mathematics and Physics and in the last decades they turned out to be of fundamental importance in the study of…
The noncommutative fractional Fourier law in bounded and unbounded domains
Fabrizio Colombo, Denis Deniz González, Stefano Pinton
Using the spectral theory on the -spectrum it is possible to define the fractional powers of a large class of vector operators. This possibility leads to new fractional diffusio…
On a polyanalytic a approach to noncommutative de Branges-Rovnyak spaces and Schur analysis
Daniel Alpay, Fabrizio Colombo, Kamal Diki +1
In this paper we begin the study of Schur analysis and de Branges-Rovnyak spaces in the framework of Fueter hyperholomorphic functions. The difference with other approaches is that…
Gauss sums, superoscillations and the Talbot carpet
F. Colombo, I. Sabadini, D. C. Struppa +1
We consider the evolution, for a time-dependent Schrödinger equation, of the so called Dirac comb. We show how this evolution allows us to recover explicitly (indeed optically) the…