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Titolo: | Strong asymptotics for extremal polynomials associated with weights on R / / edited by Doron S. Lubinsky, Edward B. Saff |
Pubblicazione: | Berlin, Germany : , : Springer, , [1988] |
©1988 | |
Edizione: | 1st ed. 1988. |
Descrizione fisica: | 1 online resource (VIII, 156 p.) |
Disciplina: | 511.66 |
Soggetto topico: | Orthogonal polynomials |
Persona (resp. second.): | LubinskyD. S <1955-> (Doron Shaul) |
SaffE. B. <1944-> | |
Note generali: | Bibliographic Level Mode of Issuance: Monograph |
Nota di contenuto: | 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. |
Sommario/riassunto: | 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. |
Titolo autorizzato: | Strong asymptotics for extremal polynomials associated with weights on R |
ISBN: | 3-540-38857-5 |
Formato: | Materiale a stampa |
Livello bibliografico | Monografia |
Lingua di pubblicazione: | Inglese |
Record Nr.: | 996466539203316 |
Lo trovi qui: | Univ. di Salerno |
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