A partial digestion of the HRT counterexample

Summary

Terence Tao discusses the Heil-Ramanathan-Topiwala (HRT) conjecture, which asserts that a nonzero function with reasonable decay cannot satisfy a finite linear relation among its time-frequency shifts. He notes that the conjecture holds when all shifts are frequency shifts or collinear. For the lattice case, commutativity allows a diagonalization that reduces the relation to a pointwise equation, using restrictions to cosets of integers. The post is a partial digestion of an HRT counterexample, but does not present the counterexample itself.