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Statement of Main Results
Potentials and Majorisation Functions
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An,R analogue of Theorem apply Assume the notation Brezis and J L choose Christoffel functions closed subsets coefficients College de France deduce denotes entire function Erdos weights estimate exists extremal errors extremal polynomials find polynomials fixed but large follows Freud weights Further given by 9.1 H Brezis Hence Hilbert space independent integral J L Lions Jackson's Theorem Lemma Let H Let W G Lipschitz condition lower bound Maclaurin series monic polynomial n large Nevai's non—negative Nonlinear partial differential Note obtain Orthogonal Polynomials partial differential equations Pn(u Pn(x polynomial of degree polynomials of Theorem positive in 1,1 positive integer positive number possibly for simple proof of Theorem real line Recall result rn(u rn(x RsQ'(Rs satisfying simple zeros Step Szego Theorem 9.1 Theorem III.l trigonometric polynomials upper bound weighted polynomials yields