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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ISBN-13
978-3-540-47792-1 (9783540477921)
DOI
Schweitzer Klassifikation
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].
