The analytic fixed point function. II.
The analytic theory of matrix orthogonal polynomials.
The analytic -capacity and the Cauchy integral
The angular distribution of mass by Bergman functions.
Let D = {z: |z| < 1} be the unit disk in the complex plane and denote by dA two-dimensional Lebesgue measure on D. For ε > 0 we define Σε = {z: |arg z| < ε}. We prove that for every ε > 0 there exists a δ > 0 such that if f is analytic, univalent and area-integrable on D, and f(0) = 0 thenThis problem arose in connection with a characterization by Hamilton, Reich and Strebel of extremal dilatation for quasiconformal homeomorphisms of D.
The angular distribution of mass by weighted Bergman functions.
The Apollonian metric: limits of the comparison and bilipschitz properties.
The Apollonian metric: uniformity and quasiconvexity.
The approximation of a polynomial's measure, with applications towards Jensen's theorem.
The area formula for -mappings
Let be a mapping in the Sobolev space . Then the change of variables, or area formula holds for provided removing from counting into the multiplicity function the set where is not approximately Hölder continuous. This exceptional set has Hausdorff dimension zero.
The area of the Mandelbrot set.
The asymptotic behavior of Green's functions for quasi-hyperbolic metrics on degenerating Riemann surfaces.
The asymptotic behaviour of certain entire functions of order zero.
The Asymptotic Value of the Circle-Packing Rigidity Constants sn .
The basic properties of Bloch functions.
The Berezin transform and operators on spaces of analytic functions
In this article we will illustrate how the Berezin transform (or symbol) can be used to study classes of operators on certain spaces of analytic functions, such as the Hardy space, the Bergman space and the Fock space. The article is organized according to the following outline. 1. Spaces of analytic functions 2. Definition and properties Berezin transform 3. Berezin transform and non-compact operators 4. Commutativity of Toeplitz operators 5. Berezin transform and Hankel or Toeplitz operators 6....
The Bergman and Schiffer transforms on weighted norm spaces
The Bieberbach Conjecture for Restricted Initial Coefficients.
The Bieberbach Conjecture for Univalent Functions with Small Second Coefficients.
The binomial theorem for hypercomplex numbers.
The Bohr inequality for ordinary Dirichlet series
We extend to the setting of Dirichlet series previous results of H. Bohr for Taylor series in one variable, themselves generalized by V. I. Paulsen, G. Popescu and D. Singh or extended to several variables by L. Aizenberg, R. P. Boas and D. Khavinson. We show in particular that, if with , then and even slightly better, and , C being an absolute constant.