Weighted Approximation with Varying Weight
Series: Lecture Notes in Mathematics; 1569;
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Product details:
- Edition number 1994
- Publisher Springer
- Date of Publication 28 February 1994
- Number of Volumes 1 pieces, Book
- ISBN 9783540577058
- Binding Paperback
- No. of pages118 pages
- Size 235x155 mm
- Weight 454 g
- Language English
- Illustrations VI, 118 p. 0
Categories
Long description:
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.
Springer Book Archives
Table of Contents:
Freud weights.- Approximation with general weights.- Varying weights.- Applications.
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Weighted Approximation with Varying Weight
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