This item is printed on demand - it takes 3-4 days longer - Neuware -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. 124 pp. Englisch.

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T�tulo: Weighted Approximation with Varying Weight
Editor: Springer Berlin Heidelberg Feb 1994
Fecha de publicaci�n: 1994
Idioma: Ingl�s
ISBN 10: 354057705X
ISBN 13: 9783540577058
Encuadernaci�n: Taschenbuch
Estado: Neu

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Sinopsis

A new construction is given for approximating a logarithmic potential by a discrete one. This yields a new approach to approximation with weighted polynomials of the form w"n"(" "= uppercase)P"n"(" "= uppercase). The new technique settles several open problems, and it leads to a simple proof 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- type asymptotics for the leading coefficients of the corresponding orthogonal polynomials. The method is also modified toyield (in a sense) uniformly good approximation on the whole support. This allows one to deduce strong asymptotics in some L p(uppercase) extremal problems with varying weights. Applications are given, relating to fast decreasing polynomials, asymptotic behavior of orthogonal polynomials and multipoint Pade approximation. The approach is potential-theoretic, but the text is self-contained.

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BuchWeltWeit Ludwig Meier e.K.
Germany

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