The book incorporates research papers and surveys written byparticipants 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, rationalapproximation of classical functions, quadrature formulas, theory of n-widths, nonlinear approximation in Hardyalgebras, numerical results on best polynomialapproximations, wavelet analysis. FROM THE CONTENTS: E.A. Rakhmanov: Strong asymptotics fororthogonal polynomials associated with exponential weightson R.- A.L. Levin, E.B. Saff: Exact Convergence Rates for Best Lp Rational Approximation to the Signum Function andfor 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 fieldsand differential forms.- O.G. Parfenov: Extremal problemsfor 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 orthogonalpolynomials.- V.N. Temlyakov: The universality of the Fibonacci cubature formulas.
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