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The Wodzicki residue for pseudo-differential operators on compact Lie groups
Duván Cardona
Let be an arbitrary compact Lie group. In this work we apply the method of the analytic continuation of traces in order to compute the Wodzicki residue for a classical pseudo-d…
Boundedness of oscillating singular integrals on Lie groups of polynomial growth
Duván Cardona, Michael Ruzhansky
We investigate the boundedness of oscillating singular integrals on Lie groups of polynomial growth in order to extend the classical oscillating conditions due to Fefferman and Ste…
Dixmier traces, Wodzicki residues, and determinants on compact Lie groups: the paradigm of the global quantisation
Duván Cardona, Julio Delgado, Michael Ruzhansky
\begin{abstract} By following the paradigm of the global quantisation, instead of the analysis under changes of coordinates, in this work we establish a global analysis for the exp…
On the index of pseudo-differential operators on compact Lie groups
Duván Cardona
In this note we study the analytical index of pseudo-differential operators by using the notion of (infinite dimensional) operator-valued symbols (in the sense of Ruzhansky and Tur…
The Dixmier trace and the noncommutative residue for multipliers on compact manifolds
Duván Cardona, César Del Corral
In this paper we give formulae for the Dixmier trace and the noncommutative residue (also called Wodzicki's residue) of pseudo-differential operators by using the notion of global…