Strong asymptotics for extremal polynomials associated with weights on ℝ

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 r...

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Detalles Bibliográficos
Autores principales: Lubinsky, Doron S, Saff, Edward B
Lenguaje:eng
Publicado: Springer 1988
Materias:
Mathematical Physics and Mathematics
Acceso en línea:https://dx.doi.org/10.1007/BFb0082413
http://cds.cern.ch/record/1691083
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author Lubinsky, Doron S
Saff, Edward B
author_facet Lubinsky, Doron S
Saff, Edward B
author_sort Lubinsky, Doron S
collection CERN
description 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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publishDate 1988
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spelling cern-16910832021-04-21T21:11:32Zdoi:10.1007/BFb0082413http://cds.cern.ch/record/1691083engLubinsky, Doron SSaff, Edward BStrong asymptotics for extremal polynomials associated with weights on ℝMathematical Physics and Mathematics0. 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.Springeroai:cds.cern.ch:16910831988
spellingShingle Mathematical Physics and Mathematics
Lubinsky, Doron S
Saff, Edward B
Strong asymptotics for extremal polynomials associated with weights on ℝ
title Strong asymptotics for extremal polynomials associated with weights on ℝ
title_full Strong asymptotics for extremal polynomials associated with weights on ℝ
title_fullStr Strong asymptotics for extremal polynomials associated with weights on ℝ
title_full_unstemmed Strong asymptotics for extremal polynomials associated with weights on ℝ
title_short Strong asymptotics for extremal polynomials associated with weights on ℝ
title_sort strong asymptotics for extremal polynomials associated with weights on ℝ
topic Mathematical Physics and Mathematics
url https://dx.doi.org/10.1007/BFb0082413
http://cds.cern.ch/record/1691083
work_keys_str_mv AT lubinskydorons strongasymptoticsforextremalpolynomialsassociatedwithweightsonr
AT saffedwardb strongasymptoticsforextremalpolynomialsassociatedwithweightsonr

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