The integral operator on the class.
The Laguerre inequality and the distribution of zeros of entire functions
The Laguerre inequality and the distribution of zeros of real entire functions are investigated with the aid of certain infinite-order differential operators. The paper includes new proofs, problems, conjectures and many illustrative examples and counterexamples.
The law of the iterated logarithm for locally univalent functions.
The length of a lemmiscate.
The limit of mappings with finite distortion.
The limit theorem for mappings with bounded distortion on the Heisenberg group and the local homeomorphism theorem.
The linear topological quasiconformality coefficient and sufficient conditions for the branch points of mappings.
The logarithmic asymptotic expansions for the norms of evaluation functionals.
The Löwner-Kufarev representations for domains with analytic boundaries
We consider the Löwner-Kufarev differential equations generating univalent maps of the unit disk onto domains bounded by analytic Jordan curves. A solution to the problem of the maximal lifetime shows how long a representation of such functions admits using infinitesimal generators analytically extendable outside the unit disk. We construct a Löwner-Kufarev chain consisting of univalent quadratic polynomials and compare the Löwner-Kufarev representations of bounded and arbitrary univalent functions....
The mapping by heights for quadratic differentials in the disk.
The multiplicity of the zero at 1 of polynomials with constrained coefficients
For n ∈ ℕ, L > 0, and p ≥ 1 let be the largest possible value of k for which there is a polynomial P ≠ 0 of the form , 1/paj ∈ ℂsuch that divides P(x). For n ∈ ℕ and L > 0 let be the largest possible value of k for which there is a polynomial P ≠ 0 of the form , , , such that divides P(x). We prove that there are absolute constants c₁ > 0 and c₂ > 0 such that for every L ≥ 1. This complements an earlier result of the authors valid for every n ∈ ℕ and L ∈ (0,1]. Essentially...
The number of connected components of certain real algebraic curves.
The Pick version of the Schwarz lemma and comparison of the Poincaré densities.
The Poisson extension of K -quasihomography on the unit circle
In this paper some estimates for the Poisson extension of a K-quasihomography on the unit circle are given.
The projective limit of the spaces
The punishing factors for convex pairs are .
The quasi-Hadamard products of uniformly convex functions defined by Dziok-Srivastava operator
The quasihyperbolic metric, growth, and John domains.
The radius of close-to-convexity of
The radius of conformity of some classes of regular functions