Kernels and Equisummation Properties of Uniformly Elliptic Operators

摘要

This reprint studies eigenfunction expansions associated with a general class of elliptic operators on R(n), and in particular, equisummation properties for expansions in eigenfunctions of pairs of operators. This analysis depends on modern techniques of operator calculus, rather than the hard classical analysis traditionally associated with equisummability. The authors apply our results to classical equisummability involving Sturm-Liouville theory, and to equiconvergence for parabolic equations. Reprints.