Asymptotics of singular values for quantum derivatives

Abstract

We obtain Weyl type asymptotics for the quantised derivative df of a function f from the homgeneous Sobolev space Ẇ, thus, providing a non-asymptotic, uniform bound on the spectrum of df. Our methods are based on the C * -algebraic notion of the principal symbol mapping on R d , as developed recently by the last two authors and collaborators.