Application of Summability Methods to Jackson Theorems for Splines

摘要

This project involved research in four mathematical areas: (1) Best local approximation in several variables for single and multi-point data sets. Hermite interpolation schemes are a special case of these schemes; (2) Analytic summability theory of eigenfunction expansions associated with singular Sturm-Liouville systems; and equisummability of eigenfunction expansions associated with elliptic operators of the same order with leading terms positive; (3) Jackson-type theorem for best one-sided approximation by one-dimensional splines; and (4) Inclusion theorems for absolute summability of divergent integrals. (Author)