Strong asymptotics for extremal polynomials associated with weights on IR /
Lubinsky, D. S. 1955-
Strong asymptotics for extremal polynomials associated with weights on IR / D.S. Lubinsky, E.B. Staff. - Berlin ; New York : Springer-Verlag, ©1988. - 1 online resource (vii, 153 pages) - Lecture notes in mathematics, 1305 0075-8434 ; . - Lecture notes in mathematics (Springer-Verlag) ; 1305. .
Includes bibliographical references (pages 146-150) and index.
Introduction -- 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 -- References -- Subject Index.
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0. The results are consequences of a strengthened form of the following assertion: Given 0 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.
Electronic reproduction.
[Place of publication not identified] :
HathiTrust Digital Library,
2010.
Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002.
http://purl.oclc.org/DLF/benchrepro0212
9783540388579 3540388575
Extremal problems (Mathematics)
Orthogonal polynomials.
Asymptotic expansions.
Problèmes extrémaux (Mathématiques)
Polynômes orthogonaux.
Développements asymptotiques.
Polinomios ortogonales
Desarrollos asintóticos
Asymptotic expansions
Extremal problems (Mathematics)
Orthogonal polynomials
Extremalpolynom
Asymptotik
Gewicht
Gewichtete Polynomapproximation
Orthogonale Polynome
Gewicht (Mathematik)
Gewichtete polynomiale Approximation.
QA3 QA331 / .L28 no. 1305
511.66
Strong asymptotics for extremal polynomials associated with weights on IR / D.S. Lubinsky, E.B. Staff. - Berlin ; New York : Springer-Verlag, ©1988. - 1 online resource (vii, 153 pages) - Lecture notes in mathematics, 1305 0075-8434 ; . - Lecture notes in mathematics (Springer-Verlag) ; 1305. .
Includes bibliographical references (pages 146-150) and index.
Introduction -- 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 -- References -- Subject Index.
Use copy
0. The results are consequences of a strengthened form of the following assertion: Given 0
Electronic reproduction.
[Place of publication not identified] :
HathiTrust Digital Library,
2010.
Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002.
http://purl.oclc.org/DLF/benchrepro0212
9783540388579 3540388575
Extremal problems (Mathematics)
Orthogonal polynomials.
Asymptotic expansions.
Problèmes extrémaux (Mathématiques)
Polynômes orthogonaux.
Développements asymptotiques.
Polinomios ortogonales
Desarrollos asintóticos
Asymptotic expansions
Extremal problems (Mathematics)
Orthogonal polynomials
Extremalpolynom
Asymptotik
Gewicht
Gewichtete Polynomapproximation
Orthogonale Polynome
Gewicht (Mathematik)
Gewichtete polynomiale Approximation.
QA3 QA331 / .L28 no. 1305
511.66