64 citations · 426 across the 29 of their papers we have counts for
5 papers · 2 filters
The zero sets of slice regular functions and the open mapping theorem
G. Gentili, C. Stoppato
A new class of regular quaternionic functions, defined by power series in a natural fashion, has been introduced in recent years. Several results of the theory recall the classical…
Extension results for slice regular functions of a quaternionic variable
Fabrizio Colombo, Graziano Gentili, Irene Sabadini +1
In this paper we prove a new representation formula for slice regular functions, which shows that the value of a slice regular function at a point can be recovered by…
A Cauchy kernel for slice regular functions
Fabrizio Colombo, Graziano Gentili, Irene Sabadini
In this paper we show how to construct a regular, non commutative Cauchy kernel for slice regular quaternionic functions. We prove an (algebraic) representation formula for such fu…
Power series and analyticity over the quaternions
G. Gentili, C. Stoppato
We study power series and analyticity in the quaternionic setting. We first consider a function f defined as the sum of a quaternionic power series centered at 0 in its domain of c…
A Phragmén - Lindelöf principle for slice regular functions
G. Gentili, C. Stoppato, D. C. Struppa
The celebrated 100-year old Phragmen-Lindelof principle is a far reaching extension of the maximum modulus theorem for holomorphic functions of one complex variable. In some recent…