Abstract
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).
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Pietsch, A. Traces and Residues of Pseudo-Differential Operators on the Torus. Integr. Equ. Oper. Theory 83, 1–23 (2015). https://doi.org/10.1007/s00020-015-2255-0
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DOI: https://doi.org/10.1007/s00020-015-2255-0