Spectral clustering properties of block multilevel Hankel matrices

By means of recent results concerning spectral distributions of Toeplitz matrices, we show that the singular values of a sequence of block p-level Hankel matrices H-n(mu), generated by a p-variate, matrix-valued measure mu whose singular part is finitely supported, are always clustered at zero, thus extending a result known when p = 1 and mu is real valued and Lipschitz continuous. The theorems hold for both eigenvalues and singular values; in the case of singular values, we allow the involved matrices to be rectangular. (C) 2000 Elsevier Science Inc. All rights reserved.