1,721,002 research outputs found
Iteration theory in hyperbolic domains
Full text linkWe study the iterates of holomorphic functions in hyperbolic domains
Vieta's formulae for regular polynomials of a quaternionic variable
Full text linkGiven 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
Regular composition for slice-regular functions of quaternionic variable
Full text linkA regular composition for slice regular function is introduced using a non commutative version of the Faa` di Bruno's Formul
The Argument Principle for Quaternionic Slice Regular Functions
Full text linkAn interesting extension of the Argument Principle is obtained for slice regular functions
A Survey on Quasiconformal Functions with Application to the Case of Functions of a Hypercomplex Variable
No full textThis survey collects the main basic results for quasiconformal functiions and aims at an extension of the definition of quasiconformality in the hypercomplex settin
The Gauss-Lucas Theorem for Regular Quaternionic Polynomials
No full textWe extend the Gauss Lucas Formula for slice regular polynomials over quaternions
Identity principles for commuting holomorphic self-maps of the unit disc
Full text linkSome identity principles for holomorphic functions are investigated
A new rigidity result for holomorphic maps
Full text linkAbstractIn this paper we determine which vanishing order of a holomorphic map f at a point of the (non necessarily regular) boundary of a very generic domain of c is required for f to be constant. In particular this vanishing order is 1 if the boundary is Dini-smooth whereas it is at least βα if f locally maps a Dini-smooth corner of opening πα into a Dini-smooth corner of opening πβ. Finally an analogous result is stated for the case of a holomorphic map f which maps a cusp into a cusp
Quaternionic Cartan coverings and applications
Full text linkWe present the topological foundation for solvability of Multiplicative
Cousin problems formulated on an axially symmetric domain In particular, we provide a geometric construction of quaternionic
Cartan coverings, which are generalizations of (complex) Cartan coverings as
presented in Section 4 of [FP]. Because of the requirements of symmetry
inherent to the domains of definition of quaternionic regular functions, the
existence of quaternionic Cartan coverings of is not a consequence of
existence of complex Cartan coverings, because for the latter there are no
requirements for the symmetries with respect to the real axis. Due to the
special role of the real axis, also the covering restricted to has to have additional properties. All these required properties
were achieved by starting from a particular symmetric tiling of the symmetric
set . Finally we provide an application
of these results to prove the vanishing of 'antisymmetric' cohomology groups of
planar symmetric domains for
Divergence zero quaternionic vector fields and Hamming graphs
Full text linkWe give a possible extension of the definition of quaternionic power
series, partial derivatives and vector fields in the case of two (and then several)
non commutative (quaternionic) variables. In this setting we also investigate
the problem of describing zero functions which are not null functions in the for-
mal sense. A connection between an analytic condition and a graph theoretic
property of a subgraph of a Hamming graph is shown, namely the condition
that polynomial vector field has formal divergence 0 is equivalent to connect-
edness of subgraphs of Hamming graphs H(d, 2). We prove that monomials in
variables z and w are always linearly independent as functions only in bidegrees
(p, 0), (p, 1), (0, q), (1, q) and (2, 2)
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