The Weyl transform of a measure

Abstract

(1) Suppose μ is a smooth measure on a smooth hypersurface of positive Gaussian curvature in R2n . If n≥ 2 , then W(μ) , the Weyl transform of μ is a compact operator, and if p> n≥ 6 , then W(μ) belongs to the p-Schatten class. (2) There exist Schatten class operators with linearly dependent quantum translates. © 2023, Indian Academy of Sciences.