On density of interpolation points, a Kadec-type theorem, and Saff's principle of contamination in \(L_ p\)-approximation

DOI10.1007/BF01208908zbMath0763.41023MaRDI QIDQ1187193

John J. Swetits, András Kroó

Publication date: 28 June 1992

Published in: Constructive Approximation (Search for Journal in Brave)

zbMATH Keywords

Lebesgue spacebest \(L_ p\)-approximationdensity of interpolation pointsSaff's principle of contaminationweighted \(L_ p\)-norm

Mathematics Subject Classification ID

Best approximation, Chebyshev systems (41A50) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65)

Related Items (13)

An analogue of Montel's theorem for some classes of rational functions ⋮ Inverse polynomial mappings and interpolation on several intervals ⋮ Improved convergence analysis of Lasserre's measure-based upper bounds for polynomial minimization on compact sets ⋮ A discrepancy theorem concerning polynomials of best approximation in \(L^ p_ w [-1, 1\)] ⋮ Some extremal problems for multivariate polynomials on convex bodies ⋮ Sequences with equi-distributed extreme points in uniform polynomial approximation ⋮ Christoffel functions on convex and starlike domains in \(\mathbb R^d\) ⋮ An SDP method for fractional semi-infinite programming problems with SOS-convex polynomials ⋮ Rational functions of best \(L_p\)-approximation and analytic continuability ⋮ Remez-type inequalities and their applications ⋮ Distribution of interpolation points of best \(L_ 2\)-approximants (\(n\)th partial sums of Fourier series) ⋮ Christoffel functions and universality on the boundary of the ball ⋮ An analogue of Montel's theorem for rational functions of best \(L_p\)-approximation

Cites Work

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• Interpolatory properties of best \(L_ 2\)-approximants
• Behavior of best \(L_ p\) polynomial approximants on the unit interval and on the unit circle
• Interpolatory properties of best \(L_ 1\)-approximants
• Interpolatory properties of best rational \(L_ 1\)-approximations
• Interlacing properties of the zeros of the error functions in best \(L^p\)- approximations
• On the distribution of points of maximal deviation in complex Cebysev approximation
• Local limiting behavior of the zeros of approximating polynomials
• Distribution of Alternation Points in Uniform Polynomial Approximation
• Weighted Polynomial Approximation of Analytic Functions
• Strong and Weak Convergence of Orthogonal Polynomials
• The Density of Extreme Points in Complex Polynomial Approximation
• The Density of Alternation Points in Rational Approximation
• Polynomial Approximation of Piecewise Analytic Functions
• Jentzsch-Szegö Type Theorems for the Zeros of Best Approximants

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