Weighted Approximation with Varying Weight

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Februar 1994



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.


Freud weights.- Approximation with general weights.- Varying weights.- Applications.
EAN: 9783540577058
ISBN: 354057705X
Untertitel: 1994. Auflage. Book. Sprache: Englisch.
Verlag: Springer
Erscheinungsdatum: Februar 1994
Seitenanzahl: 124 Seiten
Format: kartoniert
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