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Weighted Approximation with Varying Weight by Vilmos Totik

Weighted Approximation with Varying Weight

by Vilmos Totik
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Book cover type: Paperback
  • ISBN13: 9783540577058
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Springer
  • Publisher Imprint: Springer
  • Publication Date:
  • Pages: 118
  • Original Price: EUR 24.95
  • Language: English
  • Edition: 1994
  • Item Weight: 199 grams
  • BISAC Subject(s): Mathematical Analysis, Vector Analysis, and Functional Analysis

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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