Weak Chebyshev spaces and best L//1-approximation

DOI10.1016/0021-9045(83)90068-0zbMath0514.41032OpenAlexW1969851941MaRDI QIDQ1051179

Manfred Sommer

Publication date: 1983

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-9045(83)90068-0

zbMATH Keywords

generalized spline functionsuniqueness of best L1- approximationweak Chebyshev

Mathematics Subject Classification ID

Best approximation, Chebyshev systems (41A50) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65) Uniqueness of best approximation (41A52) Spline approximation (41A15) Approximation by other special function classes (41A30)

Related Items (11)

Unicity subspaces in \(L^ 1\)-approximation ⋮ One-sidedL¹Norm and Best Approximation in One-sidedL¹Norm ⋮ Examples of unicity subspaces in L₁-approximation ⋮ A general approach to the study of Chebyshev subspaces in \(L_ 1\)- approximation of continuous functions ⋮ Properties of unicity subspaces in \(L_ 1\)-approximation ⋮ Approximation by generalized splines ⋮ On Tchebysheff Systems ⋮ Finite alternation theorems and a constructive approach to piecewise polynomial approximation in Chebyshev norm ⋮ A characterization of Chebyshev spaces ⋮ Uniqueness of best \(L_ 1\)-approximations from periodic spline spaces ⋮ Some theorems on best \(L_ 1\)-approximation of continuous functions

Cites Work

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• Weak Chebyshev sets and splines
• On uniqueness of \(L_1\)-approximation for certain families of spline functions
• On the number of zeros of functions in a weak Tchebyshev-Space
• Subspaces of weak and oriented Tchebyshev-spaces
• Eigenschaften von schwach tschebyscheffschen Räumen
• The uniqueness of the element of best mean approximation to a continuous function using splines with fixed nodes
• Equioscillation under nonuniqueness in the approximation of continuous functions
• A Moment Problem in L 1 Approximation
• The Existence and Unicity of Best Approximations.
• On the approximation of real functions in the sense of P. L. Čebyšev

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