Normal view MARC view ISBD view

Lubinsky, Doron S.

Strong Asymptotics for Extremal Polynomials Associated with Weights on ℝ [electronic resource] / by Doron S. Lubinsky, Edward B. Saff. - Berlin, Heidelberg : Springer Berlin Heidelberg, 1988. - VIII, 156 p. online resource. - Lecture Notes in Mathematics, 1305 0075-8434 ; . - Lecture Notes in Mathematics, 1305 .

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.

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.

ISBN: 9783540388579

Standard No.: 10.1007/BFb0082413 doi

Subjects--Topical Terms:
Mathematics.
Numerical analysis.
Mathematics.
Numerical Analysis.

LC Class. No.: QA297-299.4

Dewey Class. No.: 518