Discrete Fourier analysis with lattices on planar domains

@article{Li2010DiscreteFA,
title={Discrete Fourier analysis with lattices on planar domains},
author={Huiyuan Li and Jiachang Sun and Yuan Xu},
journal={Numerical Algorithms},
year={2010},
volume={55},
pages={279-300}
}

A discrete Fourier analysis associated with translation lattices is developed recently by the authors. It permits two lattices, one determining the integral domain and the other determining the family of exponential functions. Possible choices of lattices are discussed in the case of lattices that tile ${{\mathbb R}}^2$ and several new results on cubature and interpolation by trigonometric, as well as algebraic, polynomials are obtained.