Strong Asymptotics for Extremal Polynomials Associated with Weights on R
Published on 9. March 1988
Book
Paperback/Softback
VIII, 156 pages
978-3-540-18958-9 (ISBN)
Description
0. The results are consequences of a strengthened form of the following assertion: Given 0 <, 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.
More details
Series
Edition
1988 ed.
Language
English
Place of publication
Berlin
Germany
Publishing group
Springer Berlin
Target group
Professional and scholarly
Research
Illustrations
VIII, 156 p.
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 10 mm
Weight
265 gr
ISBN-13
978-3-540-18958-9 (9783540189589)
DOI
10.1007/BFb0082413
Schweitzer Classification
Persons
Eli Levin is an emeritus professor at the Open University of Israel in Ramat Aviv.
Doron Lubinsky is a professor at Georgia Institute of Technology. Both are authors of papers on approximation theory, and a joint monograph on orthogonal polynomials.
Content
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.