Wave Packet Pseudomodes of Twisted Toeplitz Matrices
نویسندگان
چکیده
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, ε-pseudoeigenvectors of such matrices for exponentially small values of ε 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). c © 2004 Wiley Periodicals, Inc.
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