Weighted Approximation with Varying Weight

di Vilmos Totik (Autore)

Springer-Verlag Berlin and Heidelberg GmbH & Co. KG, 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.

• Autore: Vilmos Totik
• Editore: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
• Collana: Lecture Notes in Mathematics
• Anno: 1994
• Rilegatura: Paperback / softback
• Pagine: 118 p.
• Dimensioni: 235 x 155 mm
• EAN: 9783540577058

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