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Methods of Approximation Theory in Complex Analysis and Mathematical Physics

Leningrad, May 13-24, 1991

  • Conference proceedings
  • © 1993

Overview

Editors:
  1. Andrei A. Gonchar
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  2. Edward B. Saff
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1550)

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Table of contents (19 papers)

  1. Front Matter

    Pages I-VIII
    Download chapter PDF

  2. Bernstein theorems for harmonic functions

    • Thomas Bagby, Norman Levenberg
    Pages 7-18

  3. Spectral theory of nonlinear equations and n-widths of Sobolev spaces

    • A. P. Buslaev, V. M. Tikhomirov
    Pages 19-30

  4. On wavelet analysis

    • Charles K. Chui
    Pages 31-42

  5. Polynomials orthogonal on the unit circle with random recurrence coefficients

    • J. S. Geronimo
    Pages 43-61

  6. Using the refinement equation for the construction of pre-wavelets IV: Cube splines and elliptic splines united

    • Charles A. Micchelli
    Pages 62-70

  7. Strong asymptotics for orthogonal polynomials

    • E. A. Rakhmanov
    Pages 71-97

  8. Exact convergence rates for best L P rational approximation to the signum function and for optimal quadrature in H P

    • A. L. Levin, E. B. Saff
    Pages 98-109

  9. Uniform rational approximation of |X|

    • Herbert Stahl
    Pages 110-130

  10. Classical biorthogonal rational functions

    • Mizan Rahman, S. K. Suslov
    Pages 131-146

  11. A direct proof for Trefethen’s conjecture

    • A. I. Aptekarev
    Pages 147-148

  12. Approximation properties of harmonic vector fields and differential forms

    • V. P. Havin, A. Presa Sagué
    Pages 149-156

  13. A problem of Axler and Shields on nontangential limits and maximal ideal space of some pseudonanalytic algebras

    • Oleg V. Ivanov
    Pages 157-159

  14. Degree of approximation of analytic functions by “near the best” polynomial approximants

    • V. V. Maimeskul
    Pages 160-163

  15. Extremal problems for Blaschke products and widths

    • O. G. Parfenov
    Pages 164-168

  16. On the convergence of Bieberbach polynomials in domains with interior zero angles

    • I. E. Pritsker
    Pages 169-172

  17. Duality principle in linearized rational approximation

    • Boris Shekhtman
    Pages 173-177

  18. Universality of the fibonacci cubature formulas

    • V. N. Temlyakov
    Pages 178-184

  19. Parameters of orthogonal polynomials

    • S. Khrushchev
    Pages 185-191

  20. Some numerical results on best uniform polynomial approximation of X α on [0, 1]

    • Amos J. Carpenter, Richard S. Varga
    Pages 192-222
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Keywords

About this book

The book incorporates research papers and surveys written by participants ofan International Scientific Programme on Approximation Theory jointly supervised by Institute for Constructive Mathematics of University of South Florida at Tampa, USA and the Euler International Mathematical Instituteat St. Petersburg, Russia. The aim of the Programme was to present new developments in Constructive Approximation Theory. The topics of the papers are: asymptotic behaviour of orthogonal polynomials, rational approximation of classical functions, quadrature formulas, theory of n-widths, nonlinear approximation in Hardy algebras,numerical results on best polynomial approximations, wavelet analysis. FROM THE CONTENTS: E.A. Rakhmanov: Strong asymptotics for orthogonal polynomials associated with exponential weights on R.- A.L. Levin, E.B. Saff: Exact Convergence Rates for Best Lp Rational Approximation to the Signum Function and for Optimal Quadrature in Hp.- H. Stahl: Uniform Rational Approximation of x .- M. Rahman, S.K. Suslov: Classical Biorthogonal Rational Functions.- V.P. Havin, A. Presa Sague: Approximation properties of harmonic vector fields and differential forms.- O.G. Parfenov: Extremal problems for Blaschke products and N-widths.- A.J. Carpenter, R.S. Varga: Some Numerical Results on Best Uniform Polynomial Approximation of x on 0,1 .- J.S. Geronimo: Polynomials Orthogonal on the Unit Circle with Random Recurrence Coefficients.- S. Khrushchev: Parameters of orthogonal polynomials.- V.N. Temlyakov: The universality of the Fibonacci cubature formulas.

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