Blaschke-oscillatory equations of the form f +A(z)f = 0 ✩

We study the zero sequences of the non-trivial solutions of f +A(z)f = 0, (†) where A(z) is analytic in the unit disc. We offer several aspects illustrating the fact that it is not so uncommon for these zero sequences to be Blaschke sequences. The typical results can be divided into two categories: (1) We search for conditions on A(z) under which the zero sequences of solutions of (†) are Blaschke sequences. (2) For given Blaschke sequences satisfying certain conditions, we construct an analytic function A(z) (of minimal growth) such that these Blaschke sequences are the zero sequences of certain solutions of (†). This discussion is a continuation of the recent paper [J. Heittokangas, Solutions of f +A(z)f = 0 in the unit disc having Blaschke sequences as the zeros, Comput. Methods Funct. Theory 5 (2005) 49–63]. © 2005 Elsevier Inc. All rights reserved.