Eigenvalue decomposition for persymmetric Hankel matrices with at most three non-zero anti-diagonals

In this paper, we present an eigenvalue decomposition for any complex persymmetric Hankel matrix with at most three non-zero anti-diagonals. Furthermore, we derive a general expression for the natural powers of these Hankel matrices in terms of the natural powers of complex persymmetric anti-tridiagonal Hankel matrices.