Tangential Hilbert problem for perturbations of hyperelliptic Hamiltonian systems.
Taylor Series of the Natural Powers of the Pick Function and Applications
Tchebotaröv’s extremal problem
We give the complete solution of the extremal problem posed by N.G. Tchebotaröv in 20th of the last century, and we establish explicit parametric formulae for the extremals.
Techniques of the differential subordination for domains bounded by conic sections.
Teichmüller spaces and BMOA.
Teichmüller spaces are not starlike.
The Alexander transformation of a subclass of spirallike functions of type .
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 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 Value of the Circle-Packing Rigidity Constants sn .
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.