HRT is actually true for the hyperbolic secant function. The paper “Linear Independence of Finite Gabor Systems Determined by Behavior at Infinity” proves that HRT holds for any logarithmo-exponential function. Greeting,

Abdel

]]>https://terrytao.wordpress.com/2008/03/24/dvirs-proof-of-the-finite-field-kakeya-conjecture/

https://terrytao.wordpress.com/2016/08/24/notes-on-the-slice-rank-of-tensors/

]]>If this is what you mean, then no there is no relation between CS and Nyquist rate.

In Nyquist, the constraint on the signal is that it should be band limited however in CS, it’s constraint on the signal is different. It only should be sparse as dustin said in his reply ]]>