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Resultants of slice regular polynomials in two quaternionic variables
Anna Gori, Giulia Sarfatti, Fabio Vlacci
We introduce a non-commutative resultant, for slice regular polynomials in two quaternionic variables, defined in terms of a suitable Dieudonné determinant.We use this tool to inve…
A Strong Version of the Hilbert Nullstellensatz for slice regular polynomials in several quaternionic variables
Anna Gori, Giulia Sarfatti, Fabio Vlacci
In this paper we prove a strong version of the Hilbert Nullstellensatz in the ring of slice regular polynomials in several quaternionic variables. Our p…
Quaternionic inner and outer functions
Alessandro Monguzzi, Giulia Sarfatti, Daniel Seco
We study properties of inner and outer functions in the Hardy space of the quaternionic unit ball. In particular, we give sufficient conditions as well as necessary ones for functi…
Shift invariant subspaces of slice functions
Alessandro Monguzzi, Giulia Sarfatti
In this paper we characterize the closed invariant subspaces for the (-)multiplier operator of the quaternionic space of slice functions. As a consequence, we obtain the i…
The Mittag-Leffler Theorem for regular functions of a quaternionic variable
Graziano Gentili, Giulia Sarfatti
We prove a version of the classical Mittag-Leffler Theorem for regular functions over quaternions. Our result relies upon an appropriate notion of principal part, that is inspired…