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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Nonnegative expansions of polynomials
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by M. Wayne Wilson
Proc. Amer. Math. Soc. 24 (1970), 100-102
DOI: https://doi.org/10.1090/S0002-9939-1970-0287244-8
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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
  • Philip J. Davis, Interpolation and approximation, Blaisdell Publishing Co. [Ginn and Co.], New York-Toronto-London, 1963. MR 0157156
  • Gabor Szegö, Orthogonal polynomials, American Mathematical Society Colloquium Publications, Vol. 23, American Mathematical Society, Providence, R.I., 1959. Revised ed. MR 0106295
  • Richard S. Varga, Matrix iterative analysis, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1962. MR 0158502
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Bibliographic Information
  • © Copyright 1970 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 24 (1970), 100-102
  • MSC: Primary 42.15
  • DOI: https://doi.org/10.1090/S0002-9939-1970-0287244-8
  • MathSciNet review: 0287244