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Journal Article

On the Distribution of Extremal Points of General Chebyshev Polynomials

András Kroó and Franz Peherstorfer
Transactions of the American Mathematical Society
Vol. 329, No. 1 (Jan., 1992), pp. 117-130
DOI: 10.2307/2154079
Stable URL: http://www.jstor.org/stable/2154079
Page Count: 14

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Abstract

For a linear subspace $\mathscr{U}_n = \operatorname{span}\lbrack\varphi_1, \ldots, \varphi_n\rbrack$ in C[ a, b] we introduce general Chebyshev polynomials as solutions of the minimization problem minain - ∑n - 1i = 1 aiφi|C. For such a Chebyshev polynomial we study the distribution of its extremal points (maximum and minimum points) in terms of structural and approximative properties of Un.

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