Limiting structures for sequences of linear fractional transformations
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- by Lisa Jacobsen and W. J. Thron PDF
- Proc. Amer. Math. Soc. 99 (1987), 141-146 Request permission
Abstract:
We introduce restrained sequences of linear fractional transformations which constitute an extension of the class of continued fractions which are generally convergent. The latter concept was recently introduced by L. Jacobsen. Even for elements of the larger class, a well-defined limiting structure exists (even though such sequences need not converge). Exceptional sequences $\{ {w_n}\}$ for which $\{ {T_n}({w_n})\}$ does not have the limiting structure associated with the sequence $\{ {T_n}\}$ are also studied.References
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Constantin Carathéodory, Theory of functions of a complex variable, vol. 1, Chelsea, New York, 1954.
- Lisa Jacobsen, General convergence of continued fractions, Trans. Amer. Math. Soc. 294 (1986), no. 2, 477–485. MR 825716, DOI 10.1090/S0002-9947-1986-0825716-1
- W. J. Thron and Haakon Waadeland, Modifications of continued fractions, a survey, Analytic theory of continued fractions (Loen, 1981) Lecture Notes in Math., vol. 932, Springer, Berlin-New York, 1982, pp. 38–66. MR 690452
Additional Information
- © Copyright 1987 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 99 (1987), 141-146
- MSC: Primary 40A15; Secondary 30B70
- DOI: https://doi.org/10.1090/S0002-9939-1987-0866444-2
- MathSciNet review: 866444