Amazon cover image
Image from Amazon.com

Strong asymptotics for extremal polynomials associated with weights on IR / D.S. Lubinsky, E.B. Staff.

By: Contributor(s): Material type: TextTextSeries: Lecture notes in mathematics (Springer-Verlag) ; 1305.Publication details: Berlin ; New York : Springer-Verlag, ©1988.Description: 1 online resource (vii, 153 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9783540388579
  • 3540388575
Subject(s): Genre/Form: Additional physical formats: Print version:: Strong asymptotics for extremal polynomials associated with weights on IR.DDC classification:
  • 511.66 22
LOC classification:
  • QA3 .L28 no. 1305 QA331
Other classification:
  • *41-02
  • 41A25
  • 41A50
  • 42C05
  • MAT 418f
  • MAT 428f
  • SI 850
Online resources:
Contents:
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.
Action note:
  • digitized 2010 HathiTrust Digital Library committed to preserve
Summary: 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.
Holdings
Item type Current library Collection Call number Status Date due Barcode Item holds
eBook eBook e-Library eBook LN Mathematic Available
Total holds: 0

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 Restrictions unspecified star MiAaHDL

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.

Electronic reproduction. [Place of publication not identified] : HathiTrust Digital Library, 2010. MiAaHDL

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. MiAaHDL

http://purl.oclc.org/DLF/benchrepro0212

digitized 2010 HathiTrust Digital Library committed to preserve pda MiAaHDL

Powered by Koha