On differentiability of the operator of best \(L_ 1\)-approximation

DOI10.1016/0021-9045(84)90044-3zbMath0585.41022OpenAlexW1988257891MaRDI QIDQ1071195

András Kroó

Publication date: 1984

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

Full work available at URL: https://doi.org/10.1016/0021-9045(84)90044-3

zbMATH Keywords

best approximation operatorGatoux differentiabilityunicity subspace

Mathematics Subject Classification ID

Best approximation, Chebyshev systems (41A50) Spline approximation (41A15) Approximation by positive operators (41A36)

Cites Work

• Best \(L^1\) approximation by weak Chebyshev systems and the uniqueness of interpolating perfect splines
• The uniqueness of the element of best mean approximation to a continuous function using splines with fixed nodes
• Smoothness of approximation
• Differential properties of the operator of best approximation
• On the continuity of best approximations in the space of integrable functions
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