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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On Tchebysheff systems


Author: Kazuaki Kitahara
Journal: Proc. Amer. Math. Soc. 105 (1989), 412-418
MSC: Primary 41A05; Secondary 26A24, 41A50
MathSciNet review: 943794
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Abstract: Let $ {u_1}, \ldots ,{u_n}$ be linearly independent continuously differentiable functions on the unit interval. In this paper, we obtain the following two results. One is a necessary and sufficient condition for the span of $ \{ 1,{u_1}, \ldots ,{u_n}\} $ to have a Markoff basis containing 1. The other is that any Markoff system $ \{ {u_i}\} _{i = 1}^n$ has a Tchebysheff extension $ {u_{n + 1}}$ which is continuously differentiable.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1989-0943794-4
PII: S 0002-9939(1989)0943794-4
Keywords: Weak Tchebysheff systems, Tchebysheff systems
Article copyright: © Copyright 1989 American Mathematical Society