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Papers by Chiara Fabritiis

In this talk we discuss several features of Banach and Hilbert spaces of holomorphic functions on... more In this talk we discuss several features of Banach and Hilbert spaces of holomorphic functions on domains of such as Hardy and Bergman spaces. In particular, we study composition on generalized Bergman spaces and give results on the dynamical behaviour ( i.e. cyclicity, hypercyclicity, compactness). Special attention will be paid to underline the analogies and differences between the case of bounded and unbounded domains contained in and . [ DOI : 10.1685 / CSC06065] About DOI

Proceedings of the American Mathematical Society

According to [5] we define the *-exponential of a slice-regular function, which can be seen as a ... more According to [5] we define the *-exponential of a slice-regular function, which can be seen as a generalization of the complex exponential to quaternions. Explicit formulas for exp * (f) are provided, also in terms of suitable sine and cosine functions. We completely classify under which conditions the *-exponential of a function is either slice-preserving or CJ-preserving for some J ∈ S and show that exp * (f) is never-vanishing. Sharp necessary and sufficient conditions are given in order that exp * (f + g) = exp * (f) * exp * (g), finding an exceptional and unexpected case in which equality holds even if f and g do not commute. We also discuss the existence of a square root of a slice-preserving regular function, characterizing slice-preserving functions (defined on the circularization of simply connected domains) which admit square roots. Square roots of this kind of functions are used to provide a further formula for exp * (f). A number of examples is given throughout the paper.

In this paper we discuss several features of Hilbert spaces of holomorphic functions on domains o... more In this paper we discuss several features of Hilbert spaces of holomorphic functions on domains of Cn. We study composition and multiplication operators on generalized Bergman spaces and give results on the dynamical behaviour (i.e. cyclicity, hypercyclicity, compactness) of the first ones and on the algebraic properties of the space that the second one interprets. In particular we underline the

We prove that for a parabolic subgroup of AutBn the fixed points sets of all elements in \ {idBn ... more We prove that for a parabolic subgroup of AutBn the fixed points sets of all elements in \ {idBn } are the same. This result, together with a deep study of the structure of subgroups of AutBn acting freely and properly discontinuously on Bn , entails a generalization of the so called weak Hurwitz’s theorem: namely that, given a complex manifold X covered by Bn and such that the group of deck transformations of the covering is “sufficiently generic”, then idX is isolated in Hol(X, X). Mathematics Subject Classification (2000): 32A10, 32A40 (primary), 32H15, 32A30 (secondary).

Concrete Operators

In this paper we apply the results obtained in [3] to establish some outcomes of the study of the... more In this paper we apply the results obtained in [3] to establish some outcomes of the study of the behaviour of a class of linear operators, which include the Sylvester ones, acting on slice semi-regular functions. We first present a detailed study of the kernel of the linear operator ℒf,g (when not trivial), showing that it has dimension 2 if exactly one between f and g is a zero divisor, and it has dimension 3 if both f and g are zero divisors. Afterwards, we deepen the analysis of the behaviour of the -product, giving a complete classification of the cases when the functions fv, gv and fv gv are linearly dependent and obtaining, as a by-product, a necessary and sufficient condition on the functions f and g in order their *-product is slice-preserving. At last, we give an Embry-type result which classifies the functions f and g such that for any function h commuting with f + g and f * g, we have that h commutes with f and g, too.

The First Outstanding 50 Years of “Università Politecnica delle Marche”

European Women in Mathematics - Proceedings of the Tenth General Meeting, 2003

The theory of slice regular functions of a quaternionic variable, as presented in , extends the n... more The theory of slice regular functions of a quaternionic variable, as presented in , extends the notion of holomorphic function to the quaternionic setting. This fast growing theory is already rich of many results and has interesting applications. In this setting, the present paper is devoted to introduce and study the quaternionic counterparts of Hardy spaces of holomorphic functions of one complex variable. The basic properties of the theory of quaternionic Hardy spaces are investigated, and in particular a Poissontype representation formula, the notions of outer function, singular function and inner function are given. A quaternionic (partial) counterpart of the classical H p -factorization theorem is proved. This last result assumes a particularly interesting formulation for a large subclass of slice regular functions, where it is obtained in terms of an outer function, a singular function and a quaternionic Blaschke product.

AIP Conference Proceedings, 2004

We give a complete classication of the holomorphic self-maps of the unit ball of Cn into itself w... more We give a complete classication of the holomorphic self-maps of the unit ball of Cn into itself which commute with a given hyperbolic automorphism.

Rendiconti del Circolo Matematico di Palermo, 1991

In this work we examine the conditions which guarantee the uniqueness of a complex geodesic whose... more In this work we examine the conditions which guarantee the uniqueness of a complex geodesic whose range contains two fixed points of a holomorphic mapf of a bounded convex circular domain in itself and is contained in the fixed points set off.