Extremal Properties of Constrained Tchebychev Polynomials

Pierre, R.

Canadian journal of mathematics, Tome 38 (1986) no. 4, pp. 907-924

Résumé

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 s l and s 2 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

Détail

DOI : 10.4153/CJM-1986-044-1

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