Title

Linear Independence of Time-Frequency Translates for Ultimately Positive Functions

Speaker

Nikos Poursalidis

Topic

HRT conjecture

When

Monday, March 23, 2026 • 3:00–4:00 pm

Where

DMF 461

Format

In-person with Zoom access available at this link.

Seminar page

https://vignonoussa.com/bsu-seminar-nikos-poursalidis/

Speaker bio

Department profile

Article / Paper

arXiv:2509.04281

Joint work with

Romanos Diogenes Malikiosis

Organizers

Vignon Oussa (VOUSSA@bridgew.edu),
Xiangfei “Fei” Chen,
Mahmoud El-Hashash

Abstract

The HRT conjecture states that any finite Gabor system is linearly independent.

Here, \(T_{\tau}f(t)=f(t-\tau)\) and \(M_{\omega}f(t)=e^{2\pi i\omega t}f(t)\) denote the time and frequency shifts, respectively. In this talk, Nikos Poursalidis will discuss recent results for a special class of functions, namely ultimately positive functions. In particular, he will show that the HRT conjecture holds for any Gabor system generated by an ultimately positive function and a set consisting of exactly four points. He will also present results for Gabor systems generated by an ultimately positive function and translation sets whose frequencies satisfy at most one linear dependence over the rationals. The proofs draw on tools from Diophantine approximation, including an application of the Lonely Runner Conjecture, highlighting an interesting connection between harmonic analysis and number theory.

Joint Work

Joint work with Romanos Diogenes Malikiosis.

Keywords

Short Bio

Nikos Poursalidis works in harmonic analysis and time-frequency analysis. His recent work includes results related to the HRT conjecture and the linear independence of finite Gabor systems. More information is available on his
department profile page.

Questions? Contact the organizers:
Vignon Oussa.