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  • Proceedings of the Edinburgh Mathematical Society, Volume 38, Issue 2
  • June 1995, pp. 343-355

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

  • Holger Dette (a1)
  • DOI: http://dx.doi.org/10.1017/S001309150001912X
  • Published online: 01 January 2009
Abstract

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].

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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

4.H. Dette , Extremal properties for ultraspherical polynomials, J. Approx. Theory 76 (1994), 246273.

5.H. Dette , New identities for orthogonal polynomials on a compact interval, J. Math. Anal. Appl. 179 (1994), 547573.

6.T. S. Lau W. J. Studden , On an extremal problem of Fejér, J. Approx. Theory 53 (1988), 184194.

11.W. J. Studden , Ds-optimal designs for polynomial regression using continued fractions, Ann. Statist. 8 (1980), 11321141.

12.W. J. Studden , On a problem of Chebyshev, J. Approx. Theory 29 (1981), 253260.

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Proceedings of the Edinburgh Mathematical Society
  • ISSN: 0013-0915
  • EISSN: 1464-3839
  • URL: /core/journals/proceedings-of-the-edinburgh-mathematical-society
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