Abstract
We study the zero sequences of the non-trivial solutions of
, where A(z) is analytic in the unit disc. Namely, we consider the following two problems:
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(1)
find a growth condition on A(z) such that the zero sequence of any non-trivial solution of (*) is a Blaschke sequence
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(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.
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Heittokangas, J. Solutions of f″ + A(z)f = 0 in the Unit Disc Having Blaschke Sequences as the Zeros. Comput. Methods Funct. Theory 5, 49–63 (2005). https://doi.org/10.1007/BF03321085
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DOI: https://doi.org/10.1007/BF03321085