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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.
| Autorius: | Vilmos Totik |
| Serija: | Lecture Notes in Mathematics |
| Leidėjas: | Springer Berlin Heidelberg |
| Išleidimo metai: | 1994 |
| Knygos puslapių skaičius: | 124 |
| ISBN-10: | 354057705X |
| ISBN-13: | 9783540577058 |
| Formatas: | 235 x 155 x 8 mm. Knyga minkštu viršeliu |
| Kalba: | Anglų |
Parašykite atsiliepimą apie „Weighted Approximation with Varying Weight“
