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Proceedings of the American Mathematical Society

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

 

 

Solution of a convergence problem in the theory of $ T$-fractions


Author: Rolf M. Hovstad
Journal: Proc. Amer. Math. Soc. 48 (1975), 337-343
MSC: Primary 30A22
DOI: https://doi.org/10.1090/S0002-9939-1975-0364612-1
MathSciNet review: 0364612
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Abstract: Let $ f$ be a function, holomorphic in $ \vert z\vert < R$, where $ R > 1$, normalized by $ f(0) = 1$, and satisfying a boundedness condition of the form $ \vert f(z) - 1\vert < K$. It is proved that a certain modification of the Thron continued fraction expansion of $ f$ converges to $ f$ uniformly on any $ \vert z\vert \leq r < R$.


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DOI: https://doi.org/10.1090/S0002-9939-1975-0364612-1
Keywords: Holomorphic function, $ T$-fraction expansion, modified $ T$-fraction expansion
Article copyright: © Copyright 1975 American Mathematical Society