Methods of Approximation Theory in Complex Analysis and Mathematical Physics

Leningrad, May 13-24, 1991
Herausgegeben:Gonchar, Andrei A.; Saff, Edward B.

• Broschiertes Buch

Produktbeschreibung

The book incorporates research papers and surveys written byparticipants ofan International Scientific Programme onApproximation Theory jointly supervised by Institute forConstructive Mathematics of University of South Florida atTampa, USA and the Euler International MathematicalInstituteat St. Petersburg, Russia. The aim of theProgramme was to present new developments in ConstructiveApproximation 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 forBest Lp Rational Approximation to the Signum Function andfor Optimal Quadrature in Hp.- H. Stahl: Uniform RationalApproximation of x .- M. Rahman, S.K. Suslov: ClassicalBiorthogonal Rational Functions.- V.P. Havin, A. PresaSague: 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 PolynomialApproximation of x on 0,1 .- J.S. Geronimo: PolynomialsOrthogonal on the Unit Circle with Random RecurrenceCoefficients.- S. Khrushchev: Parameters of orthogonalpolynomials.- V.N. Temlyakov: The universality of theFibonacci cubature formulas.

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Produktdetails

• Lecture Notes in Mathematics 1550
• Verlag: Springer / Springer Berlin Heidelberg / Springer, Berlin
• Artikelnr. des Verlages: 978-3-540-56931-2
• 1993
• Seitenzahl: 228
• Erscheinungstermin: 30. Juli 1993
• Englisch
• Abmessung: 235mm x 155mm x 13mm
• Gewicht: 351g
• ISBN-13: 9783540569312
• ISBN-10: 3540569316
• Artikelnr.: 26407446

Inhaltsangabe

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].