4 citations · 18 across the 35 of their papers we have counts for
37 papers
A variation of the inverse Fueter theorem and the generalized polyanalytic Cauchy-Kovalevskaya extension of order 2
Antonino De Martino, Stefano Pinton
In this paper, we first establish a generalized Cauchy--Kovalevskaya (GCK) extension for axially polyanalytic functions of order . We prove that the extension can be written as…
A unified approach to the Dirac fine structures on the -spectrum and a connection with Gegenbauer polynomials
F. Colombo, A. De Martino, S. Pinton
This paper contributes to the recently introduced theory of fine structures on the -spectrum. We study, in a unified way, the functional calculi for axially Poly-Analytic-Harmon…
On the application of the factorized Fueter-Sce map to the slice hyperholomorphic Cauchy kernel
Antonino De Martino, Stefano Pinton
The Fueter-Sce theorem is one of the most important results in hypercomplex analysis, providing a two-step procedure for constructing axially monogenic functions starting from holo…
Functions and operators of the polyharmonic and polyanalytic Clifford fine structures on the -spectrum
Fabrizio Colombo, Antonino De Martino, Stefano Pinton
The spectral theory on the -spectrum originated to give quaternionic quantum mechanics a precise mathematical foundation and as a spectral theory for linear operators in vector…
Superoscillations in the hypercomplex setting
F. Colombo, F. Mantovani, S. Pinton +1
Superoscillatory functions represent a counterintuitive phenomenon in physics but also in mathematics, where a band-limited function oscillates faster than its highest Fourier comp…
An introduction to the fine structures on the -spectrum
Fabrizio Colombo, Antonino De Martino, Stefano Pinton +2
Holomorphic functions are fundamental in operator theory and their Cauchy formula is a crucial tool for defining functions of operators. The Fueter-Sce extension theorem (often cal…
The -functional calculi for the quaternionic fine structures of Dirac type
Fabrizio Colombo, Stefano Pinton, Peter Schlosser
In this paper, we utilize various integral representations derived from the Fueter-Sce extension theorem, to introduce novel functional calculi tailored for quaternionic operators…
Characterization of continuous homomorphisms on entire slice monogenic functions
Stefano Pinton, Peter Schlosser
This paper is inspired by a class of infinite order differential operators arising in the time evolution of superoscillations. Recently, infinite order differential operators have…
Entire monogenic functions of given proximate order and continuous homomorphisms
F. Colombo, R. S. Krausshar, S. Pinton +1
Infinite order differential operators appear in different fields of mathematics and physics. In the past decade they turned out to play a crucial role in the theory of superoscilla…
The harmonic -functional calculus based on the S-spectrum
Antonino de Martino, Stefano Pinton, Peter Schlosser
The aim of this paper is to introduce the -functional calculus for harmonic functions over the quaternions. More precisely, we give meaning to Df(T) for unbounded sectori…
Harmonic and polyanalytic functional calculi on the -spectrum for unbounded operators
Fabrizio Colombo, Antonino De Martino, Stefano Pinton
Harmonic and polyanalytic functional calculi have been recently defined for bounded commuting operators. Their definitions are based on the Cauchy formula of slice hyperholomorphic…
The fine structure of the spectral theory on the -spectrum in dimension five
Fabrizio Colombo, Antonino De Martino, Stefano Pinton +1
Holomorphic functions play a crucial role in operator theory and the Cauchy formula is a very important tool to define functions of operators. The Fueter-Sce-Qian extension theorem…
The general theory of superoscillations and supershifts in several variables
Fabrizio Colombo, Stefano Pinton, Irene Sabadini +1
In this paper we describe a general method to generate superoscillatory functions of several variables starting from a superoscillating sequence of one variable. Our results are ba…
Properties of a polyanalytic functional calculus on the -spectrum
Antonino De Martino, Stefano Pinton
The Fueter mapping theorem gives a constructive way to extend holomorphic functions of one complex variable to monogenic functions, i.e., null solutions of the generalized Cauchy-R…
A polyanalytic functional calculus of order 2 on the S-spectrum
Antonino De Martino, Stefano Pinton
The Fueter theorem provides a two step procedure to build an axially monogenic function, i.e. a null-solutions of the Cauchy-Riemann operator in , denoted by $ \math…
Axially harmonic functions and the harmonic functional calculus on the S-spectrum
Fabrizio Colombo, Antonino De Martino, Stefano Pinton +1
The spectral theory on the S-spectrum was introduced to give an appropriate mathematical setting to quaternionic quantum mechanics, but it was soon realized that there were differe…
Fractional powers of higher order vector operators on bounded and unbounded domains
Luca Baracco, Fabrizio Colombo, Marco M. Peloso +1
Using the -functional calculus for quaternionic operators, we show how to generate the fractional powers of some densely defined differential quaternionic operators of or…
Testing families of analytic discs in the unit ball
Luca Baracco, Stefano Pinton
Let be three non collinear points such that their mutual joining complex lines do not intersect the unit ball and such that the line through…
Higher order gradients of monogenic functions
Luca Baracco, Stefano Pinton
Given a monogenic function on the quaternionic algebra , the Clifford algebra or the octonionic algebra we prove that is su…
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…
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…
An extension theorem for regular functions of two quaternionic variables
Luca Baracco, Martino Fassina, Stefano Pinton
For functions of two quaternionic variables that are regular in the sense of Fueter, we establish a result similar in spirit to the Hanges and Trèves theorem. Namely, we show that…
On the Ekeland-Hofer symplectic capacities of the real bidisc
Luca Baracco, Martino Fassina, Stefano Pinton
In with the standard symplectic structure we consider the bidisc constructed as the product of two open real discs of radius . We compute explicit…