Abstract
For \(0<s<1\), let \(\Lambda \subset {\mathbb {D}}\) be a separated sequence such that \(\sum _{z_n\in \Lambda }(1-|z_n|)^s \delta _{z_n}\) is an s-Carleson measure. In this paper, we show that there exist certain analytic functions A such that the second order complex differential equation \(f''+Af=0\) admits a non-trivial solution f whose zero-sequence is \(\Lambda \), where the solution f belongs to some Möbius invariant function spaces. We strengthen a previous result from the literature.
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Communicated by Ilpo Laine.
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The work was supported by the NSF of Guangdong Province (No. 2019A1515110178), the Department of Education of Guangdong Province (No. 2017KQNCX078), the NNSF of China (No. 11720101003) and the STU SRFT (No. STF17005).
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Ye, F. Solutions of Second Order Complex Differential Equation Having Certain Pre-given Zeros. Comput. Methods Funct. Theory 21, 95–107 (2021). https://doi.org/10.1007/s40315-020-00318-9
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DOI: https://doi.org/10.1007/s40315-020-00318-9