Speaker
Description
For a differential operator on (\mathbb R^n) to be Fredholm, one also needs to impose growth condition on the symbol as (|x|\to\infty). For example, in the Shubin calculus a symbol is elliptic if it is invertible on large spheres in phase-space.
As considered in the calculus on filtered manifolds, the dilations on a graded Lie group (G) allow to assign different orders to vector fields. Moreover, the dilations give a new notion of order for the polynomials. Taking both into account, one obtains a Shubin type filtration of the algebra of differential operators with polynomial coefficients on (G). In this talk, I will introduce a tangent groupoid approach to this Shubin type calculus on graded Lie groups. Using generalized fixed point
algebras one can show a Fredholm criterion related to the Rockland condition. This is joint work with Philipp Schmitt and Ryszard Nest.
