Spectral asymptotics estimates for tensor products of pseudodifferential operators

I will illustrate results concerning the asymptotic behavior of the counting function of tensor products of operators, in the cases where the factors are either pseudodifferential operators on closed manifolds, or pseudodifferential operators of Shubin type on Rn, respectively. In particular, I will discuss the sharpness of the remainder term in the corresponding Weyl formulae. This is joint work with U. Battisti and M. Borsero.