The fundamental theorem of best approximation for logarithmic and exponential orders

DOI10.1016/0021-9045(81)90029-0zbMath0473.41014OpenAlexW1986903966MaRDI QIDQ1158586

E. Goerlich, P. Wallerath

Publication date: 1981

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

Full work available at URL: https://doi.org/10.1016/0021-9045(81)90029-0

zbMATH Keywords

Bernstein inequalityJackson inequalityK-functionallacunary Fourier seriesrate of best approximationZamansky inequality

Mathematics Subject Classification ID

Trigonometric approximation (42A10) Best approximation, Chebyshev systems (41A50) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65) Inequalities in approximation (Bernstein, Jackson, Nikol'ski?-type inequalities) (41A17) Rate of convergence, degree of approximation (41A25)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Best approximation with exponential orders and intermediate spaces
• Trigonometric approximation with exponential error orders. II: Properties of asymptotically optimal processes: Impossibility of arbitrarily good error estimates
• On the fundamental approximation theorems of D. Jackson, S.N. Bernstein and theorems of M. Zamansky and S.B. Stechkin
• A conjecture of M. Golomb on optimal and nearly-optimal linear approximation
• The characterization problem for best approximation with exponential error orders and evaluation of entropy
• Best Trigonometric Approximation, Fractional Order Derivatives and Lipschitz Classes
• An example of a best possible Zamansky type inequality with exponential order
• Classes de saturation de certains procédés d'approximation des séries de Fourier des fonctions continues et applications à quelques problèmes d'approximation

This page was built for publication: The fundamental theorem of best approximation for logarithmic and exponential orders