Methods of Approximation Theory in Complex Analysis and Mathematical Physics: Leningrad, May 13–24, 1991

Thomas Bagby, Norman Levenberg (auth.), Andrei A. Gonchar, Edward B. Saff (eds.)3540569316, 9783540569312

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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Table of contents :
Bernstein theorems for harmonic functions….Pages 7-18
Spectral theory of nonlinear equations and n -widths of Sobolev spaces….Pages 19-30
On wavelet analysis….Pages 31-42
Polynomials orthogonal on the unit circle with random recurrence coefficients….Pages 43-61
Using the refinement equation for the construction of pre-wavelets IV: Cube splines and elliptic splines united….Pages 62-70
Strong asymptotics for orthogonal polynomials….Pages 71-97
Exact convergence rates for best L P rational approximation to the signum function and for optimal quadrature in H P ….Pages 98-109
Uniform rational approximation of | X |….Pages 110-130
Classical biorthogonal rational functions….Pages 131-146
A direct proof for Trefethen’s conjecture….Pages 147-148
Approximation properties of harmonic vector fields and differential forms….Pages 149-156
A problem of Axler and Shields on nontangential limits and maximal ideal space of some pseudonanalytic algebras….Pages 157-159
Degree of approximation of analytic functions by “near the best” polynomial approximants….Pages 160-163
Extremal problems for Blaschke products and widths….Pages 164-168
On the convergence of Bieberbach polynomials in domains with interior zero angles….Pages 169-172
Duality principle in linearized rational approximation….Pages 173-177
Universality of the fibonacci cubature formulas….Pages 178-184
Parameters of orthogonal polynomials….Pages 185-191
Some numerical results on best uniform polynomial approximation of X α on [0, 1]….Pages 192-222