Non-commutative residues for anisotropic pseudo-differential operators in <f>Rn</f>

In this paper we define a non-commutative residue for the algebra of classical anisotropic pseudo-differential operators on <f>Rn</f> modulo regularizing operators. Furthermore, by means of the Weyl formula, we show that this trace coincides with the Dixmier trace on operators of order <f>−|M|</f>. [Copyright &y& Elsevier]