| 書目名稱 | Weighted Approximation with Varying Weight | | 編輯 | Vilmos Totik | | 視頻video | http://file.papertrans.cn/1022/1021966/1021966.mp4 | | 叢書名稱 | Lecture Notes in Mathematics | | 圖書封面 |  | | 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 | | 關(guān)鍵詞 | 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 |
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