Wave packet pseudomodes of twisted Toeplitz matrices
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, relate...
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| Format: | Journal article |
| Published: |
2004
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| Summary: | 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). |
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