Canonical conjugations at fixed points other than the Denjoy-Wolff point.
Canonical products of infinite order.
Cantor bouquets, explosions, and Knaster continua: dynamic of complex exponentials.
We describe some of the interesting dynamical and topological properties of the complex exponential family λez and its associated Julia sets.
Carleson measure, atomic decomposition and free interpolation from Bloch space.
Car-Pólya and Gel’fond’s theorems for
Cauchy's functional equation in restricted complex domains.
Characteristic Exponents of Rational Functions
We consider two characteristic exponents of a rational function f:ℂ̂ → ℂ̂ of degree d ≥ 2. The exponent is the average of log∥f’∥ with respect to the measure of maximal entropy. The exponent can be defined as the maximal characteristic exponent over all periodic orbits of f. We prove that if and only if f(z) is conformally conjugate to .
Characteristic function of a meromorphic function and its derivative
Characteristic functional equations of polynomials and the Morera-Carleman theorem.
Characterization of the convolution operators on quasianalytic classes of Beurling type that admit a continuous linear right inverse
Extending previous work by Meise and Vogt, we characterize those convolution operators, defined on the space of (ω)-quasianalytic functions of Beurling type of one variable, which admit a continuous linear right inverse. Also, we characterize those (ω)-ultradifferential operators which admit a continuous linear right inverse on for each compact interval [a,b] and we show that this property is in fact weaker than the existence of a continuous linear right inverse on .
Characterization of the Set of Limit Points of the Zeros of Annular Functions.
Cluster sets and boundary behavior of quasiregular mappings.
Cluster sets and essential cluster sets of meromorphic functions.
Cluster sets of analytic multivalued functions
Classical theorems about the cluster sets of holomorphic functions on the unit disc are extended to the more general setting of analytic multivalued functions, and examples are given to show that these extensions cannot be improved.
Cluster sets of arbitrary functions defined on plane sets
Cluster sets of arbitrary functions in Euclidean spaces (Preliminary communication)
Cluster sets of set-mappings
Cluster values of analytic functions along paths.
Coefficient multipliers on spaces of vector-valued entire Dirichlet series
The spaces of entire functions represented by Dirichlet series have been studied by Hussein and Kamthan and others. In the present paper we consider the space of all entire functions defined by vector-valued Dirichlet series and study the properties of a sequence space which is defined using the type of an entire function represented by vector-valued Dirichlet series. The main result concerns with obtaining the nature of the dual space of this sequence space and coefficient multipliers for some...
Compacts connexes invariants par une application univalente
Let K be a compact connected subset of cc, not reduced to a point, and F a univalent map in a neighborhood of K such that F(K) = K. This work presents a study and a classification of the dynamics of F in a neighborhood of K. When ℂ K has one or two connected components, it is proved that there is a natural rotation number associated with the dynamics. If this rotation number is irrational, the situation is close to that of “degenerate Siegel disks” or “degenerate Herman rings” studied by R. Pérez-Marco...