Finite sections of classical Toeplitz matrices have been heavily studied in the last decades due to its several applications in particular to engineering problems. Variable-coefficient Toeplitz matrices generalize these ones. We will present results on the asymtotic behaviour of the singular values, pseudospectrum and  the trace (in the sense of Extensions of Szegö-type theorems) for these type os sequences.

The talk is based on joint work with B. Silbermann.