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Papers by Chiara de Fabritiis

Research paper thumbnail of Applications of the Sylvester operator in the space of slice semi-regular functions

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.

Research paper thumbnail of From Canvas to Music: Mathematics as a Tool for the Composition of Jacksontime

Research paper thumbnail of Commuting Holomorphic Functions and Hyperbolic Automorphisms

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.

Research paper thumbnail of Quaternionic Hardy spaces

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.

Research paper thumbnail of Quotients of the unit ball of C n for a free action of Z

Research paper thumbnail of Quaternionic Hardy spaces

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.

Research paper thumbnail of Quotients of the unit ball of ℂn for a free action of ℤ

Journal d'Analyse Mathématique, 2001

LetBn be the unit ball ofC '~ andZ ~ P C AutB,~ be generated by a parabolic element of Aut ~,~ . ... more LetBn be the unit ball ofC '~ andZ ~ P C AutB,~ be generated by a parabolic element of Aut ~,~ . We show that the quotient ~/F is biholomorphic to a holomorphically convex domain of C", whose automorphism group is explicitly described. It follows that ~n/Z is Stein for any free action of Z.

Research paper thumbnail of On Holomorphic Maps Which Commute with Hyperbolic Automorphisms

Advances in Mathematics, 1999

Research paper thumbnail of Complex geometry of generalized annuli

Advances in Geometry, 2000

We study the complex geometry of a class of domains in C n which generalize the annuli in C, i.e.... more We study the complex geometry of a class of domains in C n which generalize the annuli in C, i.e., which are quotients of the unit ball B n of C n for the action of a group generated by a hyperbolic element of Aut B n . In particular, we prove that the degree of holomorphic maps between two such domains is bounded by a constant which depends on the ''radii'' of the domains only and we give some results on the existence of complex geodesics for the Kobayashi distance in these domains.

Research paper thumbnail of Geometry of interactions in complex bodies

Journal of Geometry and Physics, 2005

We analyze geometrical structures necessary to represent bulk and surface interactions of standar... more We analyze geometrical structures necessary to represent bulk and surface interactions of standard and substructural nature in complex bodies. Our attention is mainly focused on the influence of diffuse interfaces on sharp discontinuity surfaces. In analyzing this phenomenon, we prove the covariance of surface balances of standard and substructural interactions.

Research paper thumbnail of Applications of the Sylvester operator in the space of slice semi-regular functions

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.

Research paper thumbnail of From Canvas to Music: Mathematics as a Tool for the Composition of Jacksontime

Research paper thumbnail of Commuting Holomorphic Functions and Hyperbolic Automorphisms

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.

Research paper thumbnail of Quaternionic Hardy spaces

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.

Research paper thumbnail of Quotients of the unit ball of C n for a free action of Z

Research paper thumbnail of Quaternionic Hardy spaces

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.

Research paper thumbnail of Quotients of the unit ball of ℂn for a free action of ℤ

Journal d'Analyse Mathématique, 2001

LetBn be the unit ball ofC '~ andZ ~ P C AutB,~ be generated by a parabolic element of Aut ~,~ . ... more LetBn be the unit ball ofC '~ andZ ~ P C AutB,~ be generated by a parabolic element of Aut ~,~ . We show that the quotient ~/F is biholomorphic to a holomorphically convex domain of C", whose automorphism group is explicitly described. It follows that ~n/Z is Stein for any free action of Z.

Research paper thumbnail of On Holomorphic Maps Which Commute with Hyperbolic Automorphisms

Advances in Mathematics, 1999

Research paper thumbnail of Complex geometry of generalized annuli

Advances in Geometry, 2000

We study the complex geometry of a class of domains in C n which generalize the annuli in C, i.e.... more We study the complex geometry of a class of domains in C n which generalize the annuli in C, i.e., which are quotients of the unit ball B n of C n for the action of a group generated by a hyperbolic element of Aut B n . In particular, we prove that the degree of holomorphic maps between two such domains is bounded by a constant which depends on the ''radii'' of the domains only and we give some results on the existence of complex geodesics for the Kobayashi distance in these domains.

Research paper thumbnail of Geometry of interactions in complex bodies

Journal of Geometry and Physics, 2005

We analyze geometrical structures necessary to represent bulk and surface interactions of standar... more We analyze geometrical structures necessary to represent bulk and surface interactions of standard and substructural nature in complex bodies. Our attention is mainly focused on the influence of diffuse interfaces on sharp discontinuity surfaces. In analyzing this phenomenon, we prove the covariance of surface balances of standard and substructural interactions.