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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Chebyshev constant and Chebyshev points


Author: Susan L. Friedman
Journal: Trans. Amer. Math. Soc. 186 (1973), 129-139
MSC: Primary 52A40
MathSciNet review: 0370365
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Abstract: Using $ \lambda $th power means in the case $ \lambda \geq 1$, it is proven that the Chebyshev constant for any compact set in $ {R_n}$, real Euclidean n-space, is equal to the radius of the spanning sphere. When $ \lambda > 1$, the Chebyshev points of order m for all $ m \geq 1$ are unique and coincide with the center of the spanning sphere. For the case $ \lambda = 1$, it is established that Chebyshev points of order m for a compact set E in $ {R_2}$ are unique if and only if the cardinality of the intersection of E with its spanning circle is greater than or equal to three.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1973-0370365-6
PII: S 0002-9947(1973)0370365-6
Article copyright: © Copyright 1973 American Mathematical Society