"The HRT conjecture for four-point configurations"Okoudjou, KassoThe HRT Conjecture, proposed in 1996 by C. Heil, J. Ramanathan, and P. Topiwala, posits the linear independence of the set G(g, ?) = e2?ibk ·g(· ? ak)k = 1N for any non-zero square-integrable function g and subset ? = (ak, bk)k = 1N ? R2. Despite extensive research, the conjecture remains largely unresolved. In this talk, we focus on a special case: characterizing all four-point configurations in R2 for which the HRT Conjecture might fail for a given function. In the process, we well re-discover the significance of the (1, 3) and (2, 2) configurations introduced by Demeter. This work is a collaboration with K. Gröchenig |
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