HRT Conjecture and Linear Independence of Translates on the Heisenberg Group

TL;DR

This paper establishes an equivalence between the HRT conjecture and the linear independence of finite translates of square-integrable functions on the Heisenberg group, providing a new perspective on a longstanding problem.

Contribution

It proves the HRT conjecture is equivalent to the linear independence of finite translates on the Heisenberg group, linking two important conjectures in harmonic analysis.

Findings

HRT conjecture is equivalent to linear independence of translates

Provides a new approach to the HRT conjecture

Bridges concepts in harmonic analysis and group theory

Abstract

We prove that the HRT (Heil, Ramanathan, and Topiwala) conjecture is equivalent to the conjecture that finite translates of square-integrable functions on the Heisenberg group are linearly independent.