Bisingular $(\rho,\delta)$ pseudodifferential operators on products of compact Lie groups

Abstract

In this paper we develop the $(\rho,\delta)$ calculus of bisingular pseudodifferential operators on the product compact Lie groups, which extends the one that was earlier introduced by the second and third authors in the $(1,0)$ case. The $(\rho,\delta)$ case is the calculus suitable to construct parametrices of hypoelliptic operators on $G_1\times G_2$.