Weighted approximation with varying weight
著者
書誌事項
Weighted approximation with varying weight
（Lecture notes in mathematics, 1569）
Springer-Verlag, c1994
- : gw
- : us
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注記
Includes bibliographical references (p. [111]-114) and index
内容説明・目次
内容説明
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.
目次
Freud weights.- Approximation with general weights.- Varying weights.- Applications.
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