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Limit theorems and best constants in approximation theory. (English) Zbl 0968.41012

Anastassiou, George (ed.), Handbook of analytic-computational methods in applied mathematics. Boca Raton, FL: Chapman & Hall/CRC. 507-569 (2000).
Summary: We review various limit relations between polynomial, harmonic, and spline approximations and discuss their applications in approximation theory. We also prove some new limit theorems in \(\varphi\)-spaces and \(\mu\)-quasi-normed rearrangement-invariant spaces and apply these results to sharp constants of multidimensional approximation theory.
For the entire collection see [Zbl 0954.65001].

MSC:

41A44 Best constants in approximation theory
41A25 Rate of convergence, degree of approximation
41A63 Multidimensional problems