The Weyl Transform of a smooth measure on a real-analytic submanifold

TL;DR

This paper proves that the Weyl transform of a smooth measure supported on a non-degenerate real-analytic submanifold in n is a compact operator, revealing a connection between geometric measure support and operator properties.

Contribution

It establishes that the Weyl transform of such measures is always a compact operator, linking geometric conditions to operator theory in phase space.

Findings

Weyl transform of the measure is compact

Supports on non-degenerate real-analytic submanifolds lead to compact operators

Connects geometric measure support with operator compactness

Abstract

If $\mu$ is a smooth measure supported on a real-analytic submanifold of $\mathbb{R}^{2n}$ which is not contained in any affine hyperplane, then the Weyl transform of $\mu$ is a compact operator.