The Asymptotic Behavior of Singular Numbers of Compact Pseudodifferential Operators with Symbol Nonsmooth in Spatial Variables

Abstract

Compact pseudodifferential operators whose symbol fails to be smooth with respect to x on a given set are considered. Conditions under which Weyl’s law of spectral asymptotics remains valid for such operators are obtained. The results are applied to operators with symbols such that their order of decay as |ξ| → ∞ is a nonsmooth function of x.