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Proceedings of the American Mathematical Society

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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] Philip J. Davis, Interpolation and approximation, Blaisdell Publishing Co. Ginn and Co. New York-Toronto-London, 1963. MR 0157156
  • [2] Gabor Szegö, Orthogonal polynomials, American Mathematical Society Colloquium Publications, Vol. 23. Revised ed, American Mathematical Society, Providence, R.I., 1959. MR 0106295
  • [3] Richard S. Varga, Matrix iterative analysis, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1962. MR 0158502

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1970-0287244-8
Keywords: Expansions in orthogonal polynomials
Article copyright: © Copyright 1970 American Mathematical Society