Linear independence of time-frequency translates for ultimately positive functions

2025/09/04 by Malikiosis, Romanos Diogenes, Poursalidis, Nikos
#42C15 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2509.04281

Abstract

We prove that the HRT conjecture holds when the Gabor system consists of a 4-point set in the time-frequency plane and a square-integrable function that is ultimately positive. We also prove the conjecture for Gabor systems generated by an ultimately positive function and translation sets, whose frequencies satisfy at most one linear dependence over ℤ, improving a result of Benedetto and Bourouihiya.

Citations

• Linearly-exponential checking is enough for the Lonely Runner Conjecture and some of its variants
• Some remarks on the lonely runner conjecture
• Lonely Runner Polyhedra
• Linear Independence of Finite Gabor Systems Determined by Behavior at Infinity
• On the finite linear independence of lattice Gabor systems
• Proof of the HRT conjecture for (2,2) configurations
• Linear independence of time frequency translates for special configurations
• The lonely runner with seven runners
• Von Neumann algebras and linear independence of translates

Related

• Proof of the HRT conjecture for (2,2) configurations
• The HRT conjecture for a class of meromorphic functions
• Linear Independence of Finite Gabor Systems Determined by Behavior at Infinity
• Extension and restriction principles for the HRT conjecture
• HRT Conjecture and Linear Independence of Translates on the Heisenberg Group