8 papers · 1 filter
Fractional -Laplacian of holomorphic functions via Jacobi polynomials
Fabrizio Colombo, Antonino De Martino, Alberto Debernardi Pinos
We give a distributional definition of the -fractional Laplacian for smooth functions with power-type singularities at the origin, including negative monomials and cer…
Nonlocal Fourier Laws for Heat Propagation via Fractional powers of Vector Operators
Fabrizio Colombo, Francesco Mantovani, Peter Schlosser
The present work is devoted to the study of fractional powers of vector operators, with particular emphasis on the gradient operator with non-constant coefficients. Within the sett…
The resolvent equations for the Harmonic and bi-Harmonic functional calculi in dimension five
Fabrizio Colombo, Antonino De Martino, Joao Marques Da Costa
The fine structures on the -spectrum constitute a new research area that includes a class of functional calculi based on the -spectrum and on integral transforms determined b…
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…
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…
Spectral properties of the gradient operator with nonconstant coefficients
Fabrizio Colombo, Francesco Mantovani, Peter Schlosser
In mathematical physics, the gradient operator with nonconstant coefficients encompasses various models, including Fourier's law for heat propagation and Fick's first law, that rel…
Interpolation between domains of powers of operators in quaternionic Banach spaces
Fabrizio Colombo, Peter Schlosser
In contrast to the classical complex spectral theory, where the spectrum is related to the invertibility of , in the noncomm…
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…