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Weighted Approximation with Varying Weight / by Vilmos Totik
(Lecture Notes in Mathematics. ISSN:16179692 ; 1569)

1st ed. 1994.
出版者 Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
出版年 1994
大きさ VI, 118 p : online resource
著者標目 *Totik, Vilmos author
SpringerLink (Online service)
件 名 LCSH:Functions of real variables
LCSH:Potential theory (Mathematics)
FREE:Real Functions
FREE:Potential Theory
一般注記 Freud weights -- Approximation with general weights -- Varying weights -- Applications
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
HTTP:URL=https://doi.org/10.1007/BFb0076133
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分 類 LCC:QA331.5
DC23:515.8
書誌ID 4000109527
ISBN 9783540483236

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