Weighted Approximation with Varying Weight

1994
ISBN: 978-3-540-57705-8
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 1569, 118 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 201 g

Reihe: Lecture Notes in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Totik, Vilmos

Fachgebiete

• Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Kybernetik, Systemtheorie, Komplexe Systeme
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen
• Mathematik | Informatik Mathematik Mathematik Interdisziplinär Systemtheorie

Inhaltsverzeichnis

Freud weights.- Approximation with general weights.- Varying weights.- Applications.