Interpolatory tight wavelet frames with prime dilation

We introduce the prime coset sum method for constructing tight wavelet frames, which allows one to construct nonseparable multivariate tight wavelet frames with prime dilation, using a univariate lowpass mask with this same prime dilation as input. This method relies on the idea of finding a sum of hermitian squares representation for a nonnegative trigonometric polynomial related to the sub-QMF condition for the lowpass mask. We prove the existence of these representations under some conditions on the input lowpass mask, utilizing the special structure of the recently introduced prime coset sum method, which is used to generate the lowpass masks in our construction. We also prove guarantees on the vanishing moments of the wavelets arising from this method, some of which hold more generally.