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

 

A unified theory for real vs. complex rational Chebyshev approximation on an interval


Authors: Arden Ruttan and Richard S. Varga
Journal: Trans. Amer. Math. Soc. 312 (1989), 681-697
MSC: Primary 41A20; Secondary 30C15, 41A50
MathSciNet review: 948196
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Abstract: A unified approach is presented for determining all the constants $ {\gamma _{m,n}}\;(m \geq 0,n \geq 0)$ which occur in the study of real vs. complex rational Chebyshev approximation on an interval. In particular, it is shown that $ {\gamma _{m,m + 2}} = 1/3\;(m \geq 0)$, a problem which had remained open.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1989-0948196-7
PII: S 0002-9947(1989)0948196-7
Keywords: Rational functions, best uniform approximation, real vs. complex approximation of real functions, alternation sets
Article copyright: © Copyright 1989 American Mathematical Society