Nichteuklidischer Nullstellenabstand der Lösungen von \(w''+p(z)w=0\). (Noneuclidean distance of zeros of solutions of \(w''+p(z)w=0)\)
type: Item
instance of: scholarly article
title: Nichteuklidischer Nullstellenabstand der Lösungen von \(w''+p(z)w=0\). (Noneuclidean distance of zeros of solutions of \(w''+p(z)w=0)\)
zbMATH Open document ID: 0717.34013
DOI: 10.1007/BF01446919
published in: Mathematische Annalen
publication date: 1990-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164711
review text: The author discusses the noneuclidean distance of zeros of the equation \((1)\quad w''+p(z)w=0\) and obtains the following main result: Theorem. If the coefficient p(z) in the differential equation (1) satisfies the inequality \(| p(z)| \leq (1+\alpha^ 2)/(1-| z|^ 2)^ 2\) in D, \(D:=\{z|| z| <1\}\), then the noneuclidean distance between two zeros \(z_ 1\) and \(z_ 2\) of a nontrivial solution of (1) is \([z_ 1,z_ 2]\geq \pi /\alpha,\) and this estimation is best possible.
Mathematics Subject Classification ID: 34M99
Mathematics Subject Classification ID: 34C10
zbMATH DE Number: 4181772
zbMATH Keywords: noneuclidean distance of zeros
zbMATH Keywords: estimation is best possible
author: Horst Herold
MaRDI profile type: Publication
cites work: Remarks on a paper by Zeev Nehari
cites work: The Schwarzian derivative and schlicht functions
cites work: Complex Nonoscillation Theorems and Criteria of Univalence
cites work: Allgemeiner Sturmscher Vergleichssatz
cites work: Anwendung des Vergleichssatzes aufk-Diskonjugiertheit
description: scientific article; zbMATH DE number 4181772