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weighted approximation with varying weight
Totik (Author)
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weighted approximation with varying weight - totik
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Synopsis "weighted approximation with varying weight"
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 wn( = uppercase)pn( = 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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The book is written in English.
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