5 papers
The Corona Problem for Slice Holomorphic Functions via the Matrix Corona Problem
Fabrizio Colombo, Elodie Pozzi, Irene Sabadini +1
In this paper we prove the Corona theorem for slice hyperholomorphic functions in a general way that applies to functions with values in a Clifford algebra for any $n…
Operator model and a trace formula for pairs of unitary operators
Daniel Alpay, Fabrizio Colombo, Izchak Lewkowicz +1
Using the theory of reproducing kernel Hilbert spaces introduced by L. de Branges and J. Rovnyak we prove a trace formula for pairs of operators in Hilbert space in terms of a Cara…
The Corona Problem for Slice Hyperholomorphic Functions
Fabrizio Colombo, Elodie Pozzi, Irene Sabadini +1
This paper addresses the Corona problem for slice hyperholomorphic functions for a single quaternionic variable. While the Corona problem is well-understood in the context of one c…
New Taylor and Laurent series of axially harmonic, Fueter regular and polyanalytic functions
Fabrizio Colombo, Antonino De Martino, Irene Sabadini
The Fueter-Sce mapping theorem stands as one of the most profound outcomes in complex and hypercomplex analysis, producing hypercomplex generalizations of holomorphic functions. In…
The -resolvent estimates for the Dirac operator on hyperbolic and spherical spaces
Ivan Beschastnyi, Fabrizio Colombo, Simão Andrade Lucas +1
This seminal paper marks the beginning of our investigation into on the spectral theory based on -spectrum applied to the Dirac operator on manifolds. Specifically, we examine i…