Weighted Approximation with Varying Weight
Totik, Vilmos
| Autor: | Totik, Vilmos |
|---|---|
| Veröffentlichungsdatum: | 28.02.1994 |
| EAN: | 9783540577058 |
| Sprache: | Englisch |
| Seitenzahl: | 124 |
| Produktart: | Kartoniert / Broschiert |
| Verlag: | Springer Springer-Verlag GmbH |
Produktinformationen "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 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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