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].
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 |