Variable-coefficient Toeplitz matrices
Variable-coefficient Toeplitz matrices are generated by smooth functions defined on some compact cylinder. Familiar Toeplitz matrices with continuous generating function (defined on the complex unit circle) actually form a very particular class of such matrices and one may ask what asymptotic properties of Toeplitz matrices are valid in this more general context. To this end we describe the structure of the C*-algebra generated by variable-coefficient Toeplitz matrices and study a few spectral quantities (Szegö-like theorems, stability, pseudospectra). The talk is based on joint work with Olga Zabroda and extends earlier results of Kac/Murdock/Szegö and Zabroda/Simonenko.
