双角Gabor框架与Zauner猜想
Biangular Gabor frames and Zauner's conjecture
摘要：
二十年前，Zauner证明了对于每一维$d$，存在一个由$\mathbb{C}^d$中的$d^2$向量组成的等角紧框架。迄今为止的大多数进展都明确地在各个维度上构建了所承诺的框架，现在看来，佐纳猜想的建设性证明可能需要斯塔克猜想的进展。在本文中，我们提出了一种替代的方法，涉及双角的Gabor框架，最终可能导致一个无条件的非建设性证明Zauner猜想。
英文摘要：
Two decades ago, Zauner conjectured that for every dimension $d$, there exists an equiangular tight frame consisting of $d^2$ vectors in $\mathbb{C}^d$. Most progress to date explicitly constructs the promised frame in various dimensions, and it now appears that a constructive proof of Zauner's conjecture may require progress on the Stark conjectures. In this paper, we propose an alternative approach involving biangular Gabor frames that may eventually lead to an unconditional non-constructive proof of Zauner's conjecture.
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