Properties of multilevel block -circulants

In a previous paper we characterized unilevel block α-circulants , Am∈Cd1×d2, 0⩽m⩽n-1, in terms of the discrete Fourier transform FA={F0,F1,…,Fn-1} of A={A0,A1…,An-1}, defined by . We showed that most theoretical and computational problems concerning A can be conveniently studied in terms of corresponding problems concerning the Fourier coefficients F0,F1,…,Fn-1 individually. In this paper we show that analogous results hold for (k+1)-level matrices, where the first k levels have block circulant structure and the entries at the (k+1)-st level are unstructured rectangular matrices.