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Extremal Properties of Constrained Tchebychev Polynomials

Published online by Cambridge University Press:  20 November 2018

R. Pierre
R. Pierre*
Affiliation:
Université Laval, Québec, Québec
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In the sequel, πn will denote the class of real polynomials of degree at most n and ‖f(x)‖∞ the L∞-norm of a function on [–l, +1].

In a series of recent papers, Saff and Varga studied the properties of the so-called incomplete polynomials; that is to say polynomials of the form

where sl and s2 are fixed integers and q ∊ πn.

In there, they define the constrained Tchebychev polynomial as being, up to a multiplicative constant, the solution of the following minimization problem

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 38 , Issue 4 , 01 August 1986 , pp. 907 - 924
Copyright
Copyright © Canadian Mathematical Society 1986

References

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