Xi-Nan Dai

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math.FA2026

The Minimum Cardinality of a Dependent Finite Gabor System Is Four

Xinan Dai, Wenhao Deng, Yingdong Shi +2

Recent work produced a linearly dependent system of twelve time--frequency shifts of a Schwartz function, disproving the HRT conjecture. We show that four shifts already suffice, a…

math.FA2026

Bounded Representatives in Critical Sobolev-Hodge Spaces

Xinan Dai, Wenhao Deng, Yidong Shi +2

Let $n \geq 2$ , $1 \leq ℓ \leq n - 1$ , and $1 < p < \infty$ . We prove that every $v \in W ˙^{n / p, p} (R^{n}; Λ^{ℓ})$ has a representative $u \in W ˙^{n / p, p} \cap L^{\infty}$ with $…