Spectra of multilevel toeplitz matrices: Advanced theory via simple matrix relationships

We consider the eigenvalue and singular-value distributions for m-level Toeplitz matrices generated by a complex-valued periodic function ƒ of m real variables. We show that familiar formulations for ƒ L∞ (due to Szegő and others) can be preserved so long as f L1, and what is more, with G. Weylʹs definitions just a bit changed. In contrast to other approaches, the one we follow is based on simple matrix relationships.