当前位置: X-MOL 学术Bull. Lond. Math. Soc. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
On Gabor orthonormal bases over finite prime fields
Bulletin of the London Mathematical Society ( IF 0.9 ) Pub Date : 2020-10-28 , DOI: 10.1112/blms.12426
Alex Iosevich 1 , Mihalis Kolountzakis 2 , Yurii Lyubarskii 3 , Azita Mayeli 4 , Jonathan Pakianathan 1
Affiliation  

We study Gabor orthonormal windows in L 2 ( Z p d ) for translation and modulation sets, where p is prime and d 2 . We prove that for a set E Z p d , the indicator function 1 E is a Gabor window if and only if E tiles and is spectral. Moreover, we prove that for any function g : Z p d C with support E , if the cardinality of E coincides with the cardinality of the modulation set or if g is positive, then | g | = c 1 E , for some constant c > 0 , and E tiles and is spectral. We also prove the existence of a Gabor window g with full support where neither | g | nor | g ̂ | is an indicator function and the cardinality of the modulation set is much smaller than p d . We conclude the paper with an example and open questions.

中文翻译:

关于有限素场上的Gabor正交基

我们研究Gabor正交窗口 大号 2个 ž p d 用于转换和调制集,其中 p 是素数 d 2个 。我们证明了 E ž p d ,指标功能 1个 E 是Gabor窗口,当且仅当 E 平铺,并且是光谱。而且,我们证明对于任何功能 G ž p d C 在支持下 E ,如果 E 与调制集的基数一致,或者 G 是肯定的,那么 | G | = C 1个 E ,对于一些常数 C > 0 , 和 E 平铺,并且是光谱。我们还证明了Gabor窗口的存在 G 在没有任何人的全力支持下 | G | 也不 | G ̂ | 是一个指标函数,调制集的基数比 p d 。我们以一个示例结束本文并提出一些问题。
更新日期:2020-10-28
down
wechat
bug