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A note on some peculiar nonlinear extremal phenomena of the Chebyshev polynomials

Published online by Cambridge University Press:  20 January 2009

Holger Dette
Holger Dette
Affiliation:
Institut für Mathematische Stochastik, Abteilung Mathematik, Technische Universität Dresden, Mommsenstr, 13, 01062 Dresden, Germany
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Abstract

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We consider the problem of maximizing the sum of squares of the leading coefficients of polynomials (where Pj(x) is a polynomial of degree j) under the restriction that the sup-norm of is bounded on the interval [ −b, b] (b>0). A complete solution of the problem is presented using duality theory of convex analysis and the theory of canonical moments. It turns out, that contrary to many other extremal problems the structure of the solution will depend heavily on the size of the interval [ −b, b].

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 38 , Issue 2 , June 1995 , pp. 343 - 355
Copyright
Copyright © Edinburgh Mathematical Society 1995

References

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