Strong Asymptotics for Extremal Polynomials Associated with Weights on ℝ

✍ Scribed by Doron S. Lubinsky, Edward B. Saff (auth.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 1988
• Tongue: English
• Leaves: 159
• Series: Lecture Notes in Mathematics 1305
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Introduction....Pages 1-11
Notation and index of notation....Pages 12-16
Statement of main results....Pages 17-23
Weighted polynomials and zeros of extremal polynomials....Pages 24-27
Integral equations....Pages 28-39
Polynomial approximation of potentials....Pages 40-48
Infinite-finite range inequalities and their sharpness....Pages 49-56
The largest zeros of extremal polynomials....Pages 57-66
Further properties of U n, R (x)....Pages 67-72
Nth root asymptotics for extremal polynomials....Pages 73-79
Approximation by certain weighted polynomials, I....Pages 80-90
Approximation by certain weighted polynomials, II....Pages 91-110
Bernstein's formula and bernstein extremal polynomials....Pages 111-119
Proof of the asymptotics for E np (W)....Pages 120-127
Proof of the asymptotics for the L p extremal polynomials....Pages 128-135
The case p=2 : Orthonormal polynomials....Pages 136-145

✦ Subjects

Numerical Analysis