13 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 -resolvent estimates for the Spinor Dirac operator on manifolds with boundary conditions
Ivan Beschastnyi, Fabrizio Colombo, Simao Andrade Lucas +1
The aim of this paper is to show that the spectral theory based on the S-spectrum is particularly well suited for the Dirac operator on manifolds, even in cases where the operator…
Generalized partial-slice monogenic functions: the octonionic case
Zhenghua Xu, Irene Sabadini
In a recent paper [Trans. Amer. Math. Soc. 378 (2025), 851-883], the concept of generalized partial-slice monogenic (or regular) function was introduced over Clifford algebras. The…
Octonionic Riesz-Dunford functional calculus
Qinghai Huo, Guangbin Ren, Irene Sabadini +1
The Riesz-Dunford functional calculus over the algebra of octonions, denoted by , has long been an open problem due to the nonassociativity of octonions. Two core obsta…
On the Fueter-Sce theorem and Cauchy-Kovalevskaya extensions over alternative -algebras
Qinghai Huo, Irene Sabadini, Zhenghua Xu
Recently, the concept of generalized partial-slice monogenic (or regular) functions has been introduced and studied over Clifford algebras and octonions, respectively. In this pape…