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Strong Asymptotics for Extremal Polynomials Associated with Weights on R / by Doron S. Lubinsky, Edward B. Saff
(Lecture Notes in Mathematics. ISSN:16179692 ; 1305)
Edition | 1st ed. 1988. |
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Publisher | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer |
Year | 1988 |
Size | VIII, 156 p : online resource |
Authors | *Lubinsky, Doron S author Saff, Edward B author SpringerLink (Online service) |
Subjects | LCSH:Numerical analysis FREE:Numerical Analysis |
Notes | Notation and index of notation -- Statement of main results -- Weighted polynomials and zeros of extremal polynomials -- Integral equations -- Polynomial approximation of potentials -- Infinite-finite range inequalities and their sharpness -- The largest zeros of extremal polynomials -- Further properties of Un, R(x) -- Nth root asymptotics for extremal polynomials -- Approximation by certain weighted polynomials, I -- Approximation by certain weighted polynomials, II -- Bernstein's formula and bernstein extremal polynomials -- Proof of the asymptotics for Enp(W) -- Proof of the asymptotics for the Lp extremal polynomials -- The case p=2 : Orthonormal polynomials 0. The results are consequences of a strengthened form of the following assertion: Given 0 <p<, f Lp ( ) and a certain sequence of positive numbers associated with Q(x), there exist polynomials Pn of degree at most n, n = 1,2,3..., such that if and only if f(x) = 0 for a.e. 1. Auxiliary results include inequalities for weighted polynomials, and zeros of extremal polynomials. The monograph is fairly self-contained, with proofs involving elementary complex analysis, and the theory of orthogonal and extremal polynomials. It should be of interest to research workers in approximation theory and orthogonal polynomials HTTP:URL=https://doi.org/10.1007/BFb0082413 |
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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 | 9783540388579 |
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EB00209669 |
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Material Type | E-Book |
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Classification | LCC:QA297-299.4 DC23:518 |
ID | 4000108758 |
ISBN | 9783540388579 |
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