A new proof of Benedicks' Theorem for the Weyl Transform

TL;DR

This paper presents a clearer proof of Benedicks' theorem related to the Weyl Transform, establishing that functions with finite measure support and finite rank Weyl transforms must be zero.

Contribution

It provides a new, more transparent proof of Benedicks' theorem for the Weyl Transform, enhancing understanding of the theorem's conditions.

Findings

The proof confirms the theorem's validity with improved clarity.

It demonstrates that finite rank Weyl transforms imply the function is zero.

The approach simplifies previous proofs and offers better insight.

Abstract

Benedicks theorem for the Weyl Transform states: 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. A new, more transparent proof of this theorem is given.