文摘
This paper is the outcome of an attempt to understand the connection between singular traces and the Wodzicki residues of pseudo-differential operators on closed Riemannian manifolds as presented in the recent monograph of Lord, Sukochev, and Zanin. Employing my technique of dyadic representations of operators, I am able to replace the mountain tour performed by Sukochev and his coauthors through a walk in a park. The crucial point is that considerations about eigenvalues are no longer involved. To simplify understanding, the new approach is demonstrated by the example of pseudo-differential operators on the d-dimensional flat torus \({\mathbb{T}^d}\). In this special case it is possible to work with global symbols (which need not be smooth). Keywords Trace Operator ideal Dyadic representation Shift-invariant linear form Pseudo-differential operator Symbol Residue Connes-trace theorem