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Record Nr. |
UNISA996466539203316 |
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Titolo |
Strong asymptotics for extremal polynomials associated with weights on R / / edited by Doron S. Lubinsky, Edward B. Saff |
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Pubbl/distr/stampa |
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Berlin, Germany : , : Springer, , [1988] |
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©1988 |
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ISBN |
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Edizione |
[1st ed. 1988.] |
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Descrizione fisica |
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1 online resource (VIII, 156 p.) |
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Collana |
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Lecture Notes in Mathematics, , 0075-8434 ; ; 1305 |
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Disciplina |
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Soggetti |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Bibliographic Level Mode of Issuance: Monograph |
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Nota di contenuto |
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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. |
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Sommario/riassunto |
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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. |
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