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.
Le informazioni nella sezione "Riassunto" possono far riferimento a edizioni diverse di questo titolo.
Freud weights.- Approximation with general weights.- Varying weights.- Applications.
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VI, 114 pages Ex-Library book in very good condition. 9783540577058 Sprache: Englisch Gewicht in Gramm: 249. Codice articolo 1166239
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Paperback. Condizione: new. Paperback. This monograph offers a new construction for approximating a logarithmic potential by a discrete one. This yields a new approach to approximation with weighted polynomials of the form wn Pn. The new technique settles several open problems. It leads to a simple proof for the strong asymptotics on some Lp 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 to yield (in a sense) uniformly good approximation on the whole support. This allows the reader to deduce strong asymptotics in some Lp extremal problems with varying weights. Applications are given, relating to fast decreasing polynomials, asymptotic behaviour of orthogonal polynomials and multipoint Pade approximation. 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. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Codice articolo 9783540577058
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Taschenbuch. Condizione: Neu. 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. Codice articolo 9783540577058
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