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Limit Theorems of Polynomial Approximation with Exponential Weights
Michael I. Ganzburg, Hampton University, VA

Memoirs of the American Mathematical Society
2008; 161 pp; softcover
Volume: 192
ISBN-10: 0-8218-4063-0
ISBN-13: 978-0-8218-4063-4
List Price: US$75
Individual Members: US$45
Institutional Members: US$60
Order Code: MEMO/192/897
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The author develops the limit relations between the errors of polynomial approximation in weighted metrics and apply them to various problems in approximation theory such as asymptotically best constants, convergence of polynomials, approximation of individual functions, and multidimensional limit theorems of polynomial approximation.

In addition he establishes new inequalities for polynomials in complex domains and new asymptotics and estimates for orthogonal polynomials with exponential weights. More detailed information on approximation properties of functions is obtained for the canonical weights \(W(x)=\exp(-|x|^\alpha),\, 0<\alpha<\infty\), and some other weights.

Table of Contents

  • Introduction
  • Statement of main results
  • Properties of harmonic functions
  • Polynomial inequalities with exponential weights
  • Entire functions of exponential type and their approximation properties
  • Polynomial interpolation and approximation of entire functions of exponential type
  • Proofs of the limit theorems
  • Applications
  • Multidimensional limit theorems of polynomial approximation with exponential weights
  • Examples
  • Appendix A. Negativity of a kernel
  • Bibliography
  • Index
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