108 citations · 443 across the 80 of their papers we have counts for
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Reproducing kernel Hilbert spaces of polyanalytic functions of infinite order
Daniel Alpay, Fabrizio Colombo, Kamal Diki +1
In this paper we introduce reproducing kernel Hilbert spaces of polyanalytic functions of infinite order. First we study in details the counterpart of the Fock space and related re…
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…
The spectral theorem for normal operators on a Clifford module
Fabrizio Colombo, David P. Kimsey
In this paper, using the recently discovered notion of the -spectrum, we prove the spectral theorem for a bounded or unbounded normal operator on a Clifford module (i.e., a two-…
The Poisson kernel and the Fourier transform of the slice monogenic Cauchy kernels
Fabrizio Colombo, Antonino De Martino, Tao Qian +1
The Fueter-Sce-Qian (FSQ for short) mapping theorem is a two-steps procedure to extend holomorphic functions of one complex variable to slice monogenic functions and to monogenic f…
The -resolvent equation and Riesz projectors for the -functional calculus
Fabrizio Colombo, Antonino De Martino, Irene Sabadini
The Fueter-Sce-Qian mapping theorem is a two steps procedure to extend holomorphic functions of one complex variable to quaternionic or Clifford algebra-valued functions in the ker…
Universality property of the -functional calculus, noncommuting matrix variables and Clifford operators
Fabrizio Colombo, Jonathan Gantner, David P. Kimsey +1
The spectral theory on the -spectrum was born out of the need to give quaternionic quantum mechanics (formulated by Birkhoff and von Neumann) a precise mathematical foundation.…