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

ISBN-13: 9783540569312 / Angielski / Miękka / 1993 / 222 str.

Andrei A. Gonchar;Edward B. Saff

Opis

The research results of an international scientific project on approximation theory are presented in this volume. Topics discussed include the asymptotic behaviour of orthogonal polynomials, quadrature formulae, the theory of n-widths and wavelet analysis.

Spis treści

Bernstein theorems for harmonic functions.- Spectral theory of nonlinear equations and n-widths of Sobolev spaces.- On wavelet analysis.- Polynomials orthogonal on the unit circle with random recurrence coefficients.- Using the refinement equation for the construction of pre-wavelets IV: Cube splines and elliptic splines united.- Strong asymptotics for orthogonal polynomials.- Exact convergence rates for best L P rational approximation to the signum function and for optimal quadrature in H P .- Uniform rational approximation of |X|.- Classical biorthogonal rational functions.- A direct proof for Trefethen’s conjecture.- Approximation properties of harmonic vector fields and differential forms.- A problem of Axler and Shields on nontangential limits and maximal ideal space of some pseudonanalytic algebras.- Degree of approximation of analytic functions by “near the best” polynomial approximants.- Extremal problems for Blaschke products and widths.- On the convergence of Bieberbach polynomials in domains with interior zero angles.- Duality principle in linearized rational approximation.- Universality of the fibonacci cubature formulas.- Parameters of orthogonal polynomials.- Some numerical results on best uniform polynomial approximation of X ? on [0, 1].