Computational Methods and Function Theory 5 (2005), No. 1, 49--63
Copyright Heldermann Verlag 2005
Janne Heittokangas
janne@math.uiuc.edu , University of Illinois at Urbana-Champaign, Department of Mathematics, 1409 W. Green St., Urbana, IL 61801, U.S.A.
We study the zero sequences of the non-trivial solutions of
(1) find a growth condition on A(z) such that the zero sequence of any non-trivial solution of (*) is a Blaschke sequence;
(2) for a given Blaschke sequence of distinct complex numbers, find a coefficient function A(z) such that (*) possesses a solution having zeros precisely at the points of this prescribed sequence.
Related to Problem (2), we illustrate the growth of the resulting function A(z), and show that there are uncountably many coefficient functions A(z) with the desired property.
Keywords: Zeros of solutions, zero distribution, zero sequences, prescribed zeros, Blaschke sequences.
MSC 2000: Primary 34M10; Secondary 30D50.
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