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Extremal Properties of Constrained Tchebychev Polynomials
Published online by Cambridge University Press: 20 November 2018
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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
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- Copyright © Canadian Mathematical Society 1986
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