The Argument Principle for Quaternionic Slice Regular Functions

An interesting extension of the Argument Principle is obtained for slice regular functions

Iteration theory in hyperbolic domains

We study the iterates of holomorphic functions in hyperbolic domains

Vieta's formulae for regular polynomials of a quaternionic variable

Given a polynomial p ∈ F[x], with F a commutative ring, classical Vieta’s Formulae explicitely determine the coefficents of p in terms of the roots of p itself. In this paper, Vieta’s For- mulae are obtained for slice–regular polynomials over the non commutative algebra of Quaternions, by applying an argument which essentially relies on the method of induction and without invoking the general theory of quasideterminants and noncommutative symmetric functions

On a Criterion of Local Invertibility and Conformality for Slice Regular Quaternionic Functions

A new criterion for local invertibility of slice regular quaternionic functions is obtained. This paper is motivated by the need to find a geometrical interpretation for analytic conditions on the real Jacobian associated with a slice regular function f. The criterion involves spherical and Cullen derivatives of f and gives rise to several geometric implications, including an application to related conformality properties

On a class of automorphisms in H2 which resemble the property of preserving volume

We give a possible extension for shears and overshears in the case of two non commutative (quaternionic) variables in relation with the associated vector fields and flows. We present a possible definition of volume preserving automorphisms, even though there is no quaternionic volume form on H2 . Using this, we determine a class of quaternionic automorphisms for which the Ander- sen-Lempert theory applies. Finally, we exhibit an example of a quaternionic automor- phism, which is not in the in the closure of the set of finite compositions of volume preserving quaternionic shears

Identity principles for commuting holomorphic self-maps of the unit disc

3Some identity principles for holomorphic functions are investigated.nonemixedF. BRACCI; R. TAURASO; VLACCI, FABIOF., Bracci; R., Tauraso; Vlacci, Fabi

Identity principles for commuting holomorphic self-maps of the unit disc

AbstractLet f,g be two commuting holomorphic self-maps of the unit disc. If f and g agree at the common Wolff point up to a certain order of derivatives (no more than 3 if the Wolff point is on the unit circle), then f≡g

Identity principles for commuting holomorphic self-maps of the unit disc

Some identity principles for holomorphic functions are investigated