A criterion for disfocality
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- by Pui-kei Wong PDF
- Proc. Amer. Math. Soc. 30 (1971), 112-114 Request permission
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
- Fritz Carlson, Quelques inégalités concernant les fonctions analytiques, Ark. Mat. Astr. Fys. 29B (1943), no. 11, 6 (French). MR 0011717
- Zeev Nehari, On the zeros of solutions of second-order linear differential equations, Amer. J. Math. 76 (1954), 689–697. MR 63514, DOI 10.2307/2372711
- Zeev Nehari, Some function-theoretic aspects of linear second-order differential equations, J. Analyse Math. 18 (1967), 259–276. MR 213531, DOI 10.1007/BF02798048
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 30 (1971), 112-114
- MSC: Primary 34.06
- DOI: https://doi.org/10.1090/S0002-9939-1971-0279365-1
- MathSciNet review: 0279365