Weighted Approximation with Varying Weight / by Vilmos Totik.

Format:

Book

Author/Creator:

Totik, V., author.

Contributor:

SpringerLink (Online service)

Series:

Lecture Notes in Mathematics, 0075-8434 ; 1569.

Lecture Notes in Mathematics, 0075-8434 ; 1569

Language:

English

Subjects (All):

Mathematics.

Potential theory (Mathematics).

Real Functions.

Potential Theory.

Local Subjects:

Real Functions.

Potential Theory.

Physical Description:

1 online resource (VI, 118 pages).

Contained In:

Springer eBooks

Place of Publication:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1994.

System Details:

text file PDF

Summary:

A new construction is given for approximating a logarithmic potential by a discrete one. This yields a new approach to approximation with weighted polynomials of the form w"n"(" "= uppercase)P"n"(" "= uppercase). The new technique settles several open problems, and it leads to a simple proof for the strong asymptotics on some L p(uppercase) extremal problems on the real line with exponential weights, which, for the case p=2, are equivalent to power- type asymptotics for the leading coefficients of the corresponding orthogonal polynomials. The method is also modified toyield (in a sense) uniformly good approximation on the whole support. This allows one to deduce strong asymptotics in some L p(uppercase) extremal problems with varying weights. Applications are given, relating to fast decreasing polynomials, asymptotic behavior of orthogonal polynomials and multipoint Pade approximation. The approach is potential-theoretic, but the text is self-contained.

Contents:

Freud weights

Approximation with general weights

Varying weights

Applications.

Other Format:

Printed edition:

ISBN:

9783540483236

Access Restriction:

Restricted for use by site license.