ASYMPTOTIC VALUES OF FUNCTIONS, ANALYTIC IN PLANAR DOMAINS
Journal Title: Проблемы анализа-Issues of Analysis - Year 2013, Vol 2, Issue 1
Abstract
In [1] W. Gross constructed the example of an entire function of infinite order whose set of asymptotic values is equal to the extended complex plain. We obtain an analog of Gross’ result for functions, analytic in planar domains of arbitrary connectivity with isolated boundary fragment.
Authors and Affiliations
E. G. Ganenkova, V. V. Starkov
A lower bound for the L_2[-1,1]-norm of the logarithmic derivative of polynomials with zeros on the unit circle
Let C be the unit circle {z:|z|= 1} and Qn(z) bean arbitrary C-polynomial (i. e., all its zeros z1, . . ., zn ∈ C). We prove that the norm of the logarithmic derivative Q′n/Qn in the complex space L2[−1,1] is greater tha...
QUASI-ISOMETRIC MAPPINGS AND THE P-MODULI OF PATH FAMILIES
In this article, we study a connection between quasiisometric mappings of n-dimensional domains and the p-moduli of path families. In particular, we obtain explicit (and sharp) estimates for the distortion of the p-modul...
РАСПРЕДЕЛЕНИЕ ЗНАЧЕНИЙ ОБОБЩЕННОЙ ФУНКЦИИ ДЕЛИТЕЛЕЙ В КЛАССАХ ВЫЧЕТОВ ПО РАСТУЩЕМУ МОДУЛЮ
В работе устанавливается асимптотическая формула с остаточным членом для распределения значений обобщенной функции делителей в классах вычетов по растущему модулю.
Harmonic mappings onto R-convex domains
The plane domain D is called R-convex if D contains each compact set bounded by two shortest sub-arcs of the radius R with endpoints w1, w2 ∈ D, |w1−w2| <= 2R. In this paper, we prove the conditions of R-convexity for im...
FOURIER COEFFICIENTS OF CONTINUOUS FUNCTIONS WITH RESPECT TO LOCALIZED HAAR SYSTEM
We construct a nontrivial example of a continuous function f* on [0, 1]² which is orthogonal to tensor products of Haar functions supported on intervals of the same length. This example clarifies the possible behaviour o...