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Nonnegative expansions of polynomials

Author: M. Wayne Wilson
Journal: Proc. Amer. Math. Soc. 24 (1970), 100-102
MSC: Primary 42.15
MathSciNet review: 0287244
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Abstract: Consider expanding a set of orthogonal polynomials $ \{ {q_i}(x)\} $ as a combination of orthogonal polynomials $ \{ {p_i}(x)\} $. A sufficient condition to ensure that the expansion coefficients are nonnegative is derived. It is shown by counter-example that it is not a necessary condition.

References [Enhancements On Off] (What's this?)

  • [1] P. J. Davis, Interpolation and approximation, Blaisdell, Waltham, Mass., 1963. MR 28 #393. MR 0157156 (28:393)
  • [2] G. Szegö, Orthogonal polynomials, Amer. Math. Soc. Colloq. Publ., vol. 23, Amer. Math. Soc. Providence, R. I., 1959. MR 1, 14; MR 21 #5029. MR 0106295 (21:5029)
  • [3] R. S. Varga, Matrix iterative analysis, Prentice-Hall, Englewood Cliffs, N. J., 1962. MR 28 #1725. MR 0158502 (28:1725)

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Keywords: Expansions in orthogonal polynomials
Article copyright: © Copyright 1970 American Mathematical Society

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