On Tchebysheff systems

Kitahara, Kazuaki

doi:10.1090/S0002-9939-1989-0943794-4

On Tchebysheff systems
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by Kazuaki Kitahara PDF

Proc. Amer. Math. Soc. 105 (1989), 412-418 Request permission

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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