SINGULAR-VALUES AND EIGENVALUES OF NON-HERMITIAN BLOCK TOEPLITZ MATRICES

The asymptotic distribution of singular values and eigenvalues of non- Hermitian block Toeplitz matrices is studied. These matrices are assoc iated with the Fourier series of an univariate function f. The asympto tic distribution of singular values is computed when f belongs to L-2 and is matrix-valued, not necessarily square. Clusters of singular val ues are also studied, and a new result is proved. Moreover, a classica l formula due to Szego concerning the asymptotic spectrum of Hermitian Toeplitz matrices is extended to the non-Hermitian block case, under the assumption that f is bounded and test functions are harmonic. Fina lly, it is proved that the class of harmonic test functions is optimal , as far as that formula is concerned. (C) 1998 Elsevier Science Inc.