Trefethen, L. N. and Chapman, S. J. (2004) Wave packet pseudomodes of twisted Toeplitz matrices. Communications in Pure and Applied Mathematics, 57 (9). pp. 1233-1264. ISSN 0010-3640
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).
|Subjects:||D - G > Difference and functional equations|
|Research Groups:||Oxford Centre for Industrial and Applied Mathematics|
|Deposited By:||Jon Chapman|
|Deposited On:||03 Oct 2006|
|Last Modified:||20 Jul 2009 14:20|
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