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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
MathSciNet review: 0364612
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Abstract: Let $f$ be a function, holomorphic in $|z| < R$, where $R > 1$, normalized by $f(0) = 1$, and satisfying a boundedness condition of the form $|f(z) - 1| < K$. It is proved that a certain modification of the Thron continued fraction expansion of $f$ converges to $f$ uniformly on any $|z| \leq r < R$.

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Keywords: Holomorphic function, <IMG WIDTH="20" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$T$">-fraction expansion, modified <IMG WIDTH="20" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img2.gif" ALT="$T$">-fraction expansion
Article copyright: © Copyright 1975 American Mathematical Society