Nonnegative expansions of polynomials
Author:
M. Wayne Wilson
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
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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.
- 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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Keywords:
Expansions in orthogonal polynomials
Article copyright:
© Copyright 1970
American Mathematical Society