Weighted Approximation with Varying Weight

Totik, Vilmos

ISBN 10: 354057705X / ISBN 13: 9783540577058

Editore: Springer 1994-02, 1994

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Dati bibliografici

• Titolo: Weighted Approximation with Varying Weight
• Editore: Springer 1994-02
• Data di pubblicazione: 1994
• Lingua: Inglese
• ISBN 10: 354057705X
• ISBN 13: 9783540577058
• Rilegatura: PF
• Condizione: New

Descrizione articolo

Riassunto

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 weights,which, 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.

Contenuti

Freud weights.- Approximation with general weights.- Varying weights.- Applications.