Wave packet pseudomodes of twisted Toeplitz matrices

Abstract

The pseudospectra of banded, nonsymmetric Toeplitz or circulant matrices with varying coefficients are considered. Such matrices are characterized by a symbol that depends on both position (x) and wave number (k). It is shown that when a certain winding number or twist condition is satisfied, related to Hörmander's commutator condition for partial differential equations, -pseudoeigenvectors of such matrices for exponentially small values of exist in the form of localized wave packets. The symbol need not be smooth with respect to x, just differentiable at a point (or less).