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Quasi extended Chebyshev spaces and weight functions. (English) Zbl 1226.65011

The main result shows that the converse for any quasi extended Chebysev space on the closed bounded interval \([a,b]\) is a quasi complete W-space on \([a,b]\). In the third section the author gives a proof of the result and some implications, such as the existence of Bernstein-type operators and integral recurrence relations for Bernstein-type bases.

MSC:

65D05 Numerical interpolation
41A50 Best approximation, Chebyshev systems
41A05 Interpolation in approximation theory
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