Riesz sequences and generalized arithmetic progressions (1711.03762v1)

Abstract: The purpose of this note is to verify that the results attained in [6] admit an extension to the multidimensional setting. Namely, for subsets of the two dimensional torus we find the sharp growth rate of the step(s) of a generalized arithmetic progression in terms of its size which may be found in an exponential systems satisfying the Riesz sequence property.