Finite Fourier transform for functions with restricted support (Q797778)

Let H denote a subgroup of G(p), the multiplicative group of invertible elements of \({\mathbb{Z}}_ p\), the ring of integers modulo p. Let f: \({\mathbb{Z}}_ p\to {\mathbb{C}}\) be a function with support contained in a coset of H, aH. The paper describes how to find subsets K of \({\mathbb{Z}}_ p\), of cardinality equal to that of H, such that f can be recovered from the values of its discrete Fourier transform restricted to K. The proofs involve analyzing the matrix associated with the discrete Fourier transform of f.