Özet:

In this note, we announce the results of our investigation on the Dixmier trace and the Wodzicki residue for pseudo-differential operators on compact manifolds. We give formulae for the Dixmier trace and the non-commutative residue (also called Wodzicki’s residue) of invariant pseudo-differential operators on compact manifolds with or without boundary. For every closed manifold, the notion of global symbol for invariant pseudo-differential operators will be based on the Fourier analysis associated to every elliptic and positive operator (developed by M. Ruzhansky, V. Turunen and J. Delgado). In particular, for each compact Lie group we will use its representation theory. For the analysis of operators on compact manifolds with boundary, we will use the non-harmonic analysis associated with boundary valued problems (developed by M. Ruzhansky, N. Tokmagambetov, and J. Delgado).

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