Methods of Approximation Theory in Complex Analysis and Mathematical Physics

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.