A Sampling Theorem for Symmetric Polygons

We present a simple construction of a set of uniqueness for the Paley-Wiener space of functions bandlimited to a symmetric 2N-sided polygonal region in the plane which consists of a union of at most N - 1 shifted lattices in the plane. The idea of the proof involves an application of a technique set forth in [2] that is based on decomposing such a bandlimited function into a combination of functions bandlimited to smaller sets. We also give a sufficient condition under which the set in question is a set of sampling and interpolation for the Paley-Wiener space and hence corresponds to a Riesz basis. This result differs from previous work on this topic, notably in [7], in that the technique is quite different and fewer shifted lattices are required.