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Blaschke-oscillatory equations of the form \(f''+A(z)f=0\). (English) Zbl 1094.34060
Summary: We study the zero sequences of the nontrivial solutions of
\[ f''+A(z)f=0, \tag† \] 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 of the author [Comput. Methods Funct. Theory 5, 49–63 (2005; Zbl 1099.34076)].

MSC:
34M10 Oscillation, growth of solutions to ordinary differential equations in the complex domain
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