Weighted approximation with varying weight
Author(s)
Bibliographic Information
Weighted approximation with varying weight
（Lecture notes in mathematics, 1569）
Springer-Verlag, c1994
- : gw
- : us
Available at / 89 libraries
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
: BerlinL/N||LNM||1569RM940401
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Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science図書
: Berlindc20:511/t642070294108
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Note
Includes bibliographical references (p. [111]-114) and index
Description and Table of Contents
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.
Table of Contents
Freud weights.- Approximation with general weights.- Varying weights.- Applications.
by "Nielsen BookData"
