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Proceedings of the American Mathematical Society

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A criterion for disfocality

Author: Pui-kei Wong
Journal: Proc. Amer. Math. Soc. 30 (1971), 112-114
MSC: Primary 34.06
MathSciNet review: 0279365
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Abstract: A linear differential equation of the second order with coefficients holomorphic in the unit disk is considered. It is shown that if the coefficients are $ {H^p}$ functions such that their norms satisfy a certain inequality, then all nontrivial solutions of the equation will be disfocal in the disk.

References [Enhancements On Off] (What's this?)

  • [1] Fritz Carlson, Quelques inégalités concernant les fonctions analytiques, Ark. Mat. Astr. Fys. 29B (1943), no. 11, 6 (French). MR 0011717
  • [2] Zeev Nehari, On the zeros of solutions of second-order linear differential equations, Amer. J. Math. 76 (1954), 689–697. MR 0063514
  • [3] Zeev Nehari, Some function-theoretic aspects of linear second-order differential equations, J. Analyse Math. 18 (1967), 259–276. MR 0213531

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Keywords: Complex differential equations, disfocal solutions, $ {H^p}$ functions
Article copyright: © Copyright 1971 American Mathematical Society