书目名称 | Weighted Approximation with Varying Weight |
编辑 | Vilmos Totik |
视频video | |
丛书名称 | Lecture Notes in Mathematics |
图书封面 |  |
描述 | A new construction is given for approximating a logarithmicpotential by adiscrete 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 thereal line with exponential weights,which, for the case p=2, are equivalent to power- typeasymptotics for the leading coefficients ofthecorresponding orthogonal polynomials. The method is alsomodified toyield (in a sense) uniformly good approximationon the whole support. Thisallows one to deduce strongasymptotics in some L p(uppercase) extremal problems withvarying weights. Applications are given, relating tofastdecreasing polynomials, asymptotic behavior of orthogonalpolynomials and multipoint Pade approximation. The approachis potential-theoretic, but the text is self-contained. |
出版日期 | Book 1994 |
关键词 | Approximation; Logarithmic potentials; Pade approximation; Varying Weight; orthogonal Polynomials |
版次 | 1 |
doi | https://doi.org/10.1007/BFb0076133 |
isbn_softcover | 978-3-540-57705-8 |
isbn_ebook | 978-3-540-48323-6Series ISSN 0075-8434 Series E-ISSN 1617-9692 |
issn_series | 0075-8434 |
copyright | Springer-Verlag Berlin Heidelberg 1994 |