Strichartz estimates for quasi-periodic functions and applications

We show Strichartz estimates for quasi-periodic functions with decaying Fourier coefficients via $\ell^2$-decoupling. When we additionally average in time, further improvements can be obtained. Next, we apply multilinear refinements to show low regularity local well-posedness for nonlinear Schr\"odinger equations. For the cubic nonlinear Schr\"odinger equation the approach yields the sharp local well-posedness result.