Yu-Chen Yang

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math.FA2026

The Complex Banach Isometric Conjecture

Xinan Dai, Wendao Deng, Yidong Shi +2

Banach asked whether a normed space must be Hilbert if, for one fixed dimension greater than one, all subspaces of that dimension are linearly isometric. We prove the complex case.…

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 $…