Analytic capacity and linear measure
Analytic capacity, Calderón-Zygmund operators, and rectifiability
For K ⊂ C compact, we say that K has vanishing analytic capacity (or γ(K) = 0) when all bounded analytic functions on CK are constant. We would like to characterize γ(K) = 0 geometrically. Easily, γ(K) > 0 when K has Hausdorff dimension larger than 1, and γ(K) = 0 when dim(K) < 1. Thus only the case when dim(K) = 1 is interesting. So far there is no characterization of γ(K) = 0 in general, but the special case when the Hausdorff measure H1(K) is finite was recently settled. In this...
Analytic families of quasi-conformal mappings
Analytic formulas for the hyperbolic distance between two contractions
In this paper we give some analytic formulas for the hyperbolic (Harnack) distance between two contractions which permit concrete computations in several situations, including the finite-dimensional case. The main consequence of these formulas is the proof of the Schwarz-Pick Lemma. It modifies those given in [13] by the avoidance of a general Schur type formula for contractive analytic functions, more exactly by reducing the case to the more manageable situation when the function takes as values...
Analytic functions of a Proper Contraction.
Analytic functions of non-Bazilevič type and starlikeness.
Analytic functions over valued fields.
Analytic Functions with Bounded Mean Oscillation and Logarithms of HP Functions.
Analytic Self-Mapping Reducing to the Identity Mapping
Angle distortion theorems for starlike and spirallike functions with respect to a boundary point.
Angles and quasiconformal mappings on Riemannian manifolds
Angular estimations of certain integral operators.
Annular bounds for polynomial zeros and Schur stability of difference equations.
Another refinement of Bernstein's inequality.
Apollonian isometries of regular domains are Möbius mappings.
Application de la méthode des fonctions algébriques à la représentation conforme [Book]
Application of Salagean and Ruscheweyh Operators on Univalent Holomorphic Functions with Finitely many Coefficients
MSC 2010: 30C45, 30C50The purpose of the present paper is to introduce a new subclass of holomorphic univalent functions with negative and fixed finitely coefficient based on Salagean and Ruscheweyh differential operators. The various results investigated in this paper include coefficient estimates, extreme points and Radii properties.
Application of Subordination Principle to Log-Harmonic alpha-spirallike Mappings
MSC 2010: 30C45, 30C55The aim of this paper is to give an application of the subordination principle to the class of spirallike logharmonic mappings which was introduced by Abdulhadi and Hengartner [1].
Application of the subordination principle to the harmonic mappings convex in one direction with shear construction method.
Applications of certain linear operators in the theory of analytic functions
The object of the present paper is to illustrate the usefulness, in the theory of analytic functions, of various linear operators which are defined in terms of (for example) fractional derivatives and fractional integrals, Hadamard product or convolution, and so on.