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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.

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  • [1] F. Carlson, Quelques inégalités concernant les fonctions analytiques, Ark. Mat. Astr. Fys. 29B (1943), no. 11, 1-6. MR 6, 205. MR 0011717 (6:205e)
  • [2] Zeev Nehari, On the zeros of solutions of second-order linear differential equations, Amer J. Math. 76 (1954), 689-697. MR 16, 131. MR 0063514 (16:131f)
  • [3] -, Some function-theoretic aspects of linear second-order differential equations, J. Analyse Math. 18 (1967), 259-276. MR 35 #4391. MR 0213531 (35:4391)

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

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