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Approximation with Rational Functions
D. J. Newman
A co-publication of the AMS and CBMS.

CBMS Regional Conference Series in Mathematics
1979; 52 pp; softcover
Number: 41
Reprint/Revision History:
reprinted 1981
ISBN-10: 0-8218-1691-8
ISBN-13: 978-0-8218-1691-2
List Price: US$25
Member Price: US$20
All Individuals: US$20
Order Code: CBMS/41
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This series of lectures treats certain amusing and interesting aspects of rational function approximations, striving for variety and diversity rather than depth or thoroughness. Graduate students and faculty, knowledgeable in the elements of real and complex analysis, should gain insight into recent developments in the field.


Table of Contents

  • Approximation to \(x^k\)
  • Müntz rational functions
  • Quadrature in \(H^p\)
  • Quadrature in \(H^p\), concluded
  • Rational approximation to \(e^x\)
  • Using only real zeros and poles
  • Approximation of Lip 1 Functions
  • Proof of the Lip 1 conjecture
  • \(e^x\) using only negative zeros and poles
  • Open problems
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