Spectral properties of variable coefficient Toeplitz matrices
Variable Toeplitz matrices, a generalization of the finite sections
of a Toeplitz operator, have received increasing interest in recent
years. They also appear under different names: generalized locally
Toeplitz matrices, generalized convolutions or twisted Toeplitz
matrices, with applications to discretized PDE, probability theory
and statiscal mechanics. We will focus on sequences of variable-
coefficient Toeplitz matrices with symbol on a class of the Wiener
type. Using C*- algebras techniques, we will discuss the asymptotic
behaviour of singular values, condition numbers and pseudospectrum,
as well as the analogon of Fredolhm theory for sequences.
