6 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 Jacobi 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…