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Representation of a Certain Classof Polynomials

Published online by Cambridge University Press:  20 November 2018

Raymond Leblanc
Raymond Leblanc*
Affiliation:
Universite du Quebec à Trois-Rivières
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In this note, we discuss a representation of the class of polynomials with real coefficients having all zeros in a given disk of the complex plane C, in terms of convex combinations of certain extremal polynomials of this class. The result stated in the theorem is known [1] for polynomials having n real zeros in the interval [a.b.]. In the following z will be a complex number and D[(a + b)/2, (b-a)/2] the closed disk of the complex plane centered at the real point (a + b)/2 and having radius (b-a)/2.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 19 , Issue 3 , 01 September 1976 , pp. 297 - 301
Copyright
Copyright © Canadian Mathematical Society 1976

References

1. Davis, C., Problem #111, Canadian Math Bulletin, Vol. 9 (1966).Google Scholar
2. Leblanc, R., Représentation des polynômes positifs sur [-1,1], Canadian Math Bulletin, Vol. 15 (4), (1972) pp. 601, 602.Google Scholar