Linearly invariant families of holomorphic mappings of a ball. The dimension reduction method.
Linearly-invariant families and generalized Meixner–Pollaczek polynomials
The extremal functions f0(z) realizing the maxima of some functionals (e.g. max |a3|, and max arg f′(z)) within the so-called universal linearly invariant family Uα (in the sense of Pommerenke [10]) have such a form that f′0(z) looks similar to generating function for Meixner-Pollaczek (MP) polynomials [2], [8]. This fact gives motivation for the definition and study of the generalized Meixner-Pollaczek (GMP) polynomials Pλn (x; θ,ψ) of a real variable x as coefficients of [###] where the parameters...
Liouville type theorems for mappings with bounded (co)-distortion
We obtain Liouville type theorems for mappings with bounded -distorsion between Riemannian manifolds. Besides these mappings, we introduce and study a new class, which we call mappings with bounded -codistorsion.
Liouville's theorem in a pseudo-conformal space.
Lipschitz Classes and the Hardy-Littlewood Property.
Lipschitz continuity of solutions of the Liouville equation. (La continuité de Lipschitz des solutions de l'équation de Liouville.)
Local convexity properties of -metric balls.
Local growth of Weierstrass -function and Whittaker-type derivative sampling.
Local inequalities for some functionals in the class S
Local stability of mappings with bounded distortion on Heisenberg groups.
Localisation de zéros de familles de trinômes
Localisation des zéros de polynômes par rapport au cercle unité
Locally biholomorphic mappings of multiconnected domains.
Locally isometric families of minimal surfaces.
Locally minimal sets for conformal dimension.
Locally uniform domains and quasiconformal mappings.
Location of the critical points of certain polynomials
Let D¯ denote the unit disk {z : |z| < 1} in the complex plane C. In this paper, we study a family of polynomials P with only one zero lying outside D¯. We establish criteria for P to satisfy implying that each of P and P' has exactly one critical point outside D¯.
Loewner chains and quasiconformal extension of holomorphic mappings
Let f(z,t) be a Loewner chain on the Euclidean unit ball B in ℂⁿ. Assume that f(z) = f(z,0) is quasiconformal. We give a sufficient condition for f to extend to a quasiconformal homeomorphism of onto itself.
Loewner-type approximations for convex functions
Logarithmic capacity is not subadditive – a fine topology approach
In Landkof’s monograph [8, p. 213] it is asserted that logarithmic capacity is strongly subadditive, and therefore that it is a Choquet capacity. An example demonstrating that logarithmic capacity is not even subadditive can be found e.gi̇n [6, Example 7.20], see also [3, p. 803]. In this paper we will show this fact with the help of the fine topology in potential theory.