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Weighted Approximation with Varying Weight / by Vilmos Totik
(Lecture Notes in Mathematics. ISSN:16179692 ; 1569)
Edition | 1st ed. 1994. |
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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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E-Book | Location | Media type | Volume | Call No. | Status | Reserve | Comments | ISBN | Printed | Restriction | Designated Book | Barcode No. |
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E-Book | オンライン | 電子ブック |
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Springer eBooks | 9783540483236 |
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