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Proceedings of the American Mathematical Society

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

 

 

Limiting structures for sequences of linear fractional transformations


Authors: Lisa Jacobsen and W. J. Thron
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
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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.


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DOI: https://doi.org/10.1090/S0002-9939-1987-0866444-2
Article copyright: © Copyright 1987 American Mathematical Society