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

Edition	1st ed. 1994.
Publisher	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
Year	1994
Size	VI, 118 p : online resource
Authors	*Totik, Vilmos author SpringerLink (Online service)
Subjects	LCSH:Functions of real variables LCSH:Potential theory (Mathematics) FREE:Real Functions FREE:Potential Theory
Notes	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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