108 citations · 443 across the 80 of their papers we have counts for
26 papers · 1 filter
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 -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…
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 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…
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-…
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.…