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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Chebyshev constant and Chebyshev points
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by Susan L. Friedman PDF
Trans. Amer. Math. Soc. 186 (1973), 129-139 Request permission

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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Additional Information
  • © Copyright 1973 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 186 (1973), 129-139
  • MSC: Primary 52A40
  • DOI: https://doi.org/10.1090/S0002-9947-1973-0370365-6
  • MathSciNet review: 0370365