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

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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 |
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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: | 20 Jul 2009 14:20 |

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