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Lecture Notes in Mathematics

Weighted Approximation with Varying Weight

Authors: Totik, Vilmos

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About this book

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 (5 chapters)

Table of contents (5 chapters)

Buy this book

eBook $29.99
price for USA in USD
  • ISBN 978-3-540-48323-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $39.95
price for USA in USD
  • ISBN 978-3-540-57705-8
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Weighted Approximation with Varying Weight
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
1569
Copyright
1994
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-48323-6
DOI
10.1007/BFb0076133
Softcover ISBN
978-3-540-57705-8
Series ISSN
0075-8434
Edition Number
1
Number of Pages
VI, 118
Topics

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