Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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



Nonnegative expansions of polynomials

Author: M. Wayne Wilson
Journal: Proc. Amer. Math. Soc. 24 (1970), 100-102
MSC: Primary 42.15
MathSciNet review: 0287244
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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?)

  • 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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 42.15

Retrieve articles in all journals with MSC: 42.15

Additional Information

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