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摘要
The main purpose of this paper is to survey some of the work on spherical approximation done by the BNU group under the direction of Professor Sun. The equiconvergent operators of Cesaro means, and their interesting applications are described. The Jackson inequality for spherical polynomials and some moduli of smoothness on the sphere are investigated. The equivalence between moduli of smoothness and K-functionals is also discussed. We also describe several weighted polynomial inequalities on the sphere, including the Remez-type and the Nikolskii-type inequalities, the Marcinkiewicz-Zygmund inequality, the Bernstein-type and the Schur-type inequalities. Positive cubature formulas on the sphere, and their relation to the Marcinkiewicz-Zygmund inequality are also discussed. A survey on recent results on asymptotic orders of the n-widths of Sobolev's classes on the sphere is also given.
- 出版日期2009-11
- 单位北京师范大学
