Schatten classes, nuclearity and nonharmonic analysis on compact manifolds with boundary

Given a compact manifold M with boundary partial derivative M, in this paper we introduce a global symbolic calculus of pseudo-differential operators associated to (M, partial derivative m). The symbols of operators with boundary conditions on partial derivative M are defined in terms of the biorthogonal expansions in eigenfunctions of a fixed operator L with the same boundary conditions on partial derivative M. The boundary partial derivative M is allowed to have (arbitrary) singularities. As an application, several criteria for the membership in Schatten classes on L-2(M) and gamma-nuclearity on L-P(M) are obtained. We also describe a new addition to the Grothendieck-Lidskii formula in this setting. Examples and applications are given to operators on M = [0, l](n) with non-periodic boundary conditions, and of operators with non-local boundary conditions. (C) 2016 The Authors. Published by Elsevier Masson SAS.