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.
Logarithmic coefficients of univalent functions.
Lower Bounds for the Zeros of Analytic Functions.
Lower Schwarz-Pick estimates and angular derivatives.
Löwnersche Differentialgleichung und quasikonform fortsetzbare schlichte Funktionen.
Löwnersche Differentialgleichung und Schlichtheitskriterien.
Lp extremal polynomials. Results and perspectives
2000 Mathematics Subject Classification: 30C40, 30D50, 30E10, 30E15, 42C05.Let α = β+γ be a positive finite measure defined on the Borel sets of C, with compact support, where β is a measure concentrated on a closed Jordan curve or on an arc (a circle or a segment) and γ is a discrete measure concentrated on an infinite number of points. In this survey paper, we present a synthesis on the asymptotic behaviour of orthogonal polynomials or Lp extremal polynomials associated to the measure α. We analyze...
Lusin's condition (N) and mappings of the class W1, n.