A gap series with growth conditions and its applications.
About a differential inequality.
Applications of the Hadamard product in geometric function theory
Let denote the set of functions holomorphic in the unit disc, normalized clasically: , whereas is an arbitrarily fixed subset. In this paper various properties of the classes , of functions of the form are studied, where , , and denotes the Hadamard product of the functions and . Some special cases of the set were considered by other authors (see, for example, [15],[6],[3]).
Conformal martingales and analytic functions.
Disques de Siegel et anneaux de Herman
Domains of ...-Holomorphy in a Separable Banach Space.
Domains with strong barrier.
Ellipses and harmonic Möbius transformations.
Extreme points and convolution properties of some classes of multivalent functions.
Geometrical properties of a family of compactifications.
Hencky-Prandtl nets and constant principal strain mappings with isolated singularities.
Higher Schwarzian operators and combinatorics of the Schwarzian derivative.
Inequalities in the complex plane.
John domains, quasidisks, and the Nehari class.
Linearization of analytic and non-analytic germs of diffeomorphisms of
Möbius-invariant metrics and generalized angles in Ptolemaic spaces.
Nonbasic harmonic maps onto convex wedges
We construct a nonbasic harmonic mapping of the unit disk onto a convex wedge. This mapping satisfies the partial differential equation where a(z) is a nontrivial extreme point of the unit ball of .
On a paper of Carleson.
On complexification and iteration of quasiregular polynomials which have algebraic degree two
We prove that each degree two quasiregular polynomial is conjugate to Q(z) = z² - (p+q)|z|² + pqz̅² + c, |p| < 1, |q| < 1. We also show that the complexification of Q can be extended to a polynomial endomorphism of ℂℙ² which acts as a Blaschke product (z-p)/(1-p̅z) · (z-q)/(1-q̅z) on ℂℙ²∖ℂ². Using this fact we study the dynamics of Q under iteration.
On the complexification of real-analytic polynomial mappings of ℝ²
We give a simple algebraic condition on the leading homogeneous term of a polynomial mapping from ℝ² into ℝ² which is equivalent to the fact that the complexification of this mapping can be extended to a polynomial endomorphism of ℂℙ². We also prove that this extension acts on ℂℙ²∖ℂ² as a quotient of finite Blaschke products.