The canonical trace and the noncommutative residue on the noncommutative torus (Q2796515)

The calculus of pseudodifferential operators on the manifolds with a continuous symmetry (e.g. the Lie groups) allows to apply the harmonic analysis technique directly to the pseudodifferential calculus. The article under review develops a foundation of the pseudodiffential calculus for the non-commutative manifolds like the \(n\)-dimensional tori introduced by \textit{M. A. Rieffel} and \textit{A. Schwarz} [Int. J. Math. 10, No. 2, 289--299 (1999; Zbl 0968.46060)]. One of the implications of the theory is a simple proof of the conformal invariance of the zeta function at zero of the Laplacian on the noncommutative torus.