Description
Springer Weighted Approximation With Varying Weight 1994 Edition by Vilmos Totik
A new construction is given for approximating a logarithmicpotential by a discrete one. This yields a new approach toapproximation with weighted polynomials of the formw"n"(" "= uppercase)P"n"(" "= uppercase). The new techniquesettles several open problems and it leads to a simpleproof for the strong asymptotics on some L p(uppercase)extremal problems on the real line with exponential weightswhich for the case p=2 are equivalent to power- typeasymptotics for the leading coefficients of thecorresponding orthogonal polynomials. The method is alsomodified toyield (in a sense) uniformly good approximationon the whole support. This allows one to deduce strongasymptotics in some L p(uppercase) extremal problems withvarying weights. Applications are given relating to fastdecreasing polynomials asymptotic behavior of orthogonalpolynomials and multipoint Pade approximation. The approachis potential-theoretic but the text is self-contained. Table of contents : Freud weights.- Approximation with general weights.- Varying weights.- Applications.