Constructive Approximation

, Volume 5, Issue 1, pp 405–414 | Cite as

On the uniqueness of canonical points in the Hobby-Rice theorem

  • András Kroó
Article

Abstract

According to the Hobby-Rice theorem for anyn-dimensional subspaceU n ofL1([a, b], ν) (ν positive, finite, nonatomic) there exist points α=s0<x1<⋯<xm+1=b, where 0≤m≤n, such that
$$\sum\limits_{j = 0}^m {( - 1)^j \int_{x_j }^{x_{j + 1} } {udv = 0,u \in U_n .} }$$
. In this paper we study under what conditions onU n the pointsx1,⋯,x m with the above property are unique for everyν. A necessary and sufficient condition for local uniqueness is found.

AMS classification

41A45 

Key words and phrases

Hobby-Rice theorem Uniqueness of canonical points Weak Chebyshev spaces 

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Copyright information

© Springer-Verlag New York Inc 1989

Authors and Affiliations

  • András Kroó
    • 1
  1. 1.Mathematical Institute of the Hungarian Academy of SciencesBudapestHungary

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