AI 中文总结
该研究证明施瓦茨函数的有限个时频平移可线性相关，构造12个时频平移的反例，否定了HRT猜想。
AI 中文摘要
我们证明施瓦茨函数的有限个时频平移可线性相关，这否定了Heil、Ramanathan和Topiwala提出的HRT猜想，具体提供了由12个时频平移构成的反例。
英文摘要
We show that a finite number of time-frequency shifts of a Schwartz function can be linearly dependent. This disproves the so-called HRT conjecture of Heil, Ramanathan, and Topiwala. In particular, we provide an example consisting of 12 time-frequency shifts.
CommentsThis version (v2) adds a separate, purely analytic proof of a qualitative counterexample, clarifying the construction mechanism; the certified numerical proof of the explicit 12-point counterexample is retained. Supplementary Python code available in the anc folder
