On non-normal solutions of linear differential equations

On non-normal solutions of linear differential equations

Normality arguments are applied to study the oscillation of solutions of f''+Af=0, where the coefficient A is analytic in the unit disc \mathbb{D} and \sup _{z\in \mathbb{D}} (1-\vert z\vert^2)^2\vert A(z)\vert < \infty . It is shown that such a differential equation may admit a non-nor...

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Veröffentlicht in:Proceedings of the American Mathematical Society 2017-03, Vol.145 (3), p.1209-1220
1. Verfasser: Janne Gröhn
Format: Artikel
Sprache:eng
Schlagworte:
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Zusammenfassung:Normality arguments are applied to study the oscillation of solutions of f''+Af=0, where the coefficient A is analytic in the unit disc \mathbb{D} and \sup _{z\in \mathbb{D}} (1-\vert z\vert^2)^2\vert A(z)\vert < \infty . It is shown that such a differential equation may admit a non-normal solution having prescribed uniformly separated zeros.
ISSN:0002-9939
1088-6826
DOI:10.1090/proc/13292