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Composition of linear fractional transformations in terms of tail sequences

Author: Lisa Jacobsen
Journal: Proc. Amer. Math. Soc. 97 (1986), 97-104
MSC: Primary 30B70; Secondary 40A15
MathSciNet review: 831395
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Abstract: We consider sequences $ \left\{ {{s_n}} \right\}$ of linear fractional transformations. Connected to such a sequence is another sequence $ \left\{ {{s_n}} \right\}$ of linear fractional transformations given by

$\displaystyle {S_n} = {s_1} \circ {s_2} \circ \cdots \circ {s_n},\quad n = 1,2,3, \ldots .$

We introduce a new way of representing $ {s_n}$ (in terms of so-called tail sequences). This representation is established to give nice expressions for $ {S_n}$. It can be seen as a generalization of the canonical form for $ {s_n}$, which gives nice expressions for

$\displaystyle {T_k} = \underbrace {{s_n} \circ {s_n} \circ \cdots \circ {s_{n.}}}_{(k{\text{ terms)}}}$

References [Enhancements On Off] (What's this?)

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Article copyright: © Copyright 1986 American Mathematical Society

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