Nichteuklidischer Nullstellenabstand der Lösungen von \(w''+p(z)w=0\). (Noneuclidean distance of zeros of solutions of \(w''+p(z)w=0)\)
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.
scientific article; zbMATH DE number 4181772