Trefethen, L. N. and Chapman, S. J. (2004) Wave packet pseudomodes of twisted Toeplitz matrices. Communications in Pure and Applied Mathematics, 57 (9). pp. 12331264. ISSN 00103640

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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).
Item Type:  Article 

Subjects:  D  G > Difference and functional equations 
Research Groups:  Oxford Centre for Industrial and Applied Mathematics 
ID Code:  296 
Deposited By:  Jon Chapman 
Deposited On:  03 Oct 2006 
Last Modified:  29 May 2015 18:19 
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