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TitleMethods of Approximation Theory in Complex Analysis and Mathematical Physics [electronic resource] : Leningrad, May 13-24, 1991 / edited by Andrei A. Gonchar, Edward B. Saff
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg, 1993
Connect tohttp://dx.doi.org/10.1007/BFb0117469
Descript 222 p. online resource

SUMMARY

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


CONTENT

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 | -- Classical biorthogonal rational functions -- A direct proof for Trefethenโ{128}{153}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 โ{128}{156}near the bestโ{128}{157} 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]


Mathematics Mathematical analysis Analysis (Mathematics) Functions of complex variables Mathematical models Physics Mathematics Functions of a Complex Variable Mathematical Modeling and Industrial Mathematics Theoretical Mathematical and Computational Physics Analysis



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