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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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Alternating Chebyshev approximation
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by Charles B. Dunham PDF
Trans. Amer. Math. Soc. 178 (1973), 95-109 Request permission

Abstract:

An approximating family is called alternating if a best Chebyshev approximation is characterized by its error curve having a certain number of alternations. The convergence properties of such families are studied. A sufficient condition for the limit of best approximation on subsets to converge uniformly to the best approximation is given: it is shown that this is often (but not always) a necessary condition. A sufficient condition for the Chebyshev operator to be continuous is given: it is shown that this is often (but not always) a necessary condition.
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Additional Information
  • © Copyright 1973 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 178 (1973), 95-109
  • MSC: Primary 41A50
  • DOI: https://doi.org/10.1090/S0002-9947-1973-0318736-8
  • MathSciNet review: 0318736