Deep zero problems and the HRT conjecture

TL;DR

This paper explores the deep zero problem in relation to the HRT conjecture, establishing a connection that leads to affirmative results for certain cases of the problem.

Contribution

It uncovers a natural link between Hedenmalm's deep zero problem and the HRT conjecture, providing new affirmative results.

Findings

Confirmed positive answers for Hedenmalm's problem 5.2 and its analogs

Established a connection between deep zero problem and HRT conjecture

Contributed to understanding time-frequency analysis problems

Abstract

We investigate a "deep zero problem" proposed by Hedenmalm. We show that there is a natural connection between Hedenmalm's problem and the classical HRT conjecture in time-frequency analysis. This connection allows us to show that Hedenmalm's problem 5.2 in [5] as well as some of its natural analogs have affirmative answers.