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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Solution of a convergence problem in the theory of $T$-fractions
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by Rolf M. Hovstad PDF
Proc. Amer. Math. Soc. 48 (1975), 337-343 Request permission

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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Additional Information
  • © Copyright 1975 American Mathematical Society
  • 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