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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Nonnormal Dirichlet quotients and nonnormal Blaschke quotients


Author: Shinji Yamashita
Journal: Proc. Amer. Math. Soc. 80 (1980), 604-606
MSC: Primary 30D45; Secondary 30D50
DOI: https://doi.org/10.1090/S0002-9939-1980-0587936-3
MathSciNet review: 587936
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Abstract: There exists a nonnormal meromorphic function $ {f_1}/{f_2}$ in $ U = \{ \vert z\vert < 1\} $, where $ {f_1}$ and $ {f_2}$ both are holomorphic functions with finite Dirichlet integrals in U. For each $ 0 < \alpha < 1$, there exists a nonnormal meromorphic function $ {B_1}/{B_2}$ in U, where $ {B_1}$ and $ {B_2}$ both are Blaschke products with finite $ \alpha $-weighted Dirichlet integrals in U.


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DOI: https://doi.org/10.1090/S0002-9939-1980-0587936-3
Article copyright: © Copyright 1980 American Mathematical Society