Fast algorithms for calculation of Gibbs derivatives on finite groups

Abstract

In this paper we discuss the definition of Gibbs derivatives on finite, not necessarily Abelian, groups in terms of the partial Gibbs derivatives. We consider the matrix representation of Gibbs derivatives defined in this way, which enables us to disclose FFT-like algorithms for the calculation of the values of Gibbs derivatives of functions on finite groups into fields admitting the existence of a Fourier transform on groups.