FAMILIES OF ELLIPTIC FUNCTIONS AND UNIFORMIZATION OF COMPLEX TORI WITH A UNIQUE POINT OVER INFINITY
Journal Title: Проблемы анализа-Issues of Analysis - Year 2018, Vol 7, Issue 2
Abstract
We investigate the problem of describing a one-parametric family of elliptic functions which uniformizes a given family of ramified coverings of the Riemann sphere with maximal possible ramification over infinity. We find a PDE for the family of functions and use it to deduce a system of ODEs for their critical points.
Authors and Affiliations
S. R. Nasyrov
Keywords
Related Articles
- EP ID EP437244
- DOI 10.15393/j3.art.2018.5290
- Views 102
- Downloads 0
РАЗЛОЖЕНИЕ ПО СОБСТВЕННЫМ ФУНКЦИЯМ ДЛЯ НЕКОТОРЫХ ФУНКЦИОНАЛЬНО-ДИФФЕРЕНЦИАЛЬНЫХ ОПЕРАТОРОВ
We prove the completness of the eigenfunctions of some boundary function-differental problems.
ПРЕОБРАЗОВАНИЕ ФУРЬЕ ФУНКЦИЙ УДОВЛЕТВОРЯЮЩИХ УСЛОВИЮ ЛИПШИЦА, НА ПЛОСКОСТИ ЛОБАЧЕВСКОГО
We prove the non-Euclidean analogue of the theorem of E. Titchmarsh about the description of image under Fourier transform of functions satisfying certain Lipschitz conditions.
ГРАНИЧНОЕ ПОВЕДЕНИЕ МЕРОМОРФНЫХ ФУНКЦИЙ В МНОГОСВЯЗНЫХ ОБЛАСТЯХ
В первой части статьи доказывается аналог теоремы Каратеодори о граничном соответствии в случае конечносвязной области. Вторая часть посвящена доказательству аналога теоремы Плеснера (о структуре предельных множеств гран...
FAMILIES OF ELLIPTIC FUNCTIONS AND UNIFORMIZATION OF COMPLEX TORI WITH A UNIQUE POINT OVER INFINITY
We investigate the problem of describing a one-parametric family of elliptic functions which uniformizes a given family of ramified coverings of the Riemann sphere with maximal possible ramification over infinity. We fin...
Multivariate Iyengar type inequalities for radial functions
Here we present a variety of multivariate Iyengar type inequalities for radial functions defined on the shell and ball. Our approach is based on the polar coordinates in R^N, N>=2, and the related multivariate polar inte...