Benedicks' Theorem for the Weyl Transform

TL;DR

This paper proves a version of Benedicks' theorem for the Weyl transform, showing that if a function's support has finite measure and its Weyl transform has finite rank, then the function must be zero.

Contribution

It establishes a new uncertainty principle for the Weyl transform, extending Benedicks' theorem to this setting.

Findings

Functions with finite measure support and finite rank Weyl transforms are identically zero.

The result generalizes classical uncertainty principles to the Weyl transform context.

Abstract

If the set of points where a function is nonzero is of finite measure, and its Weyl transform is a finite rank operator, then the function is identically zero.