WAVE PACKET PSEUDOMODES OF TWISTED TOEPLITZ MATRICES


L N TREFETHEN

Nick.Trefethen@comlab.ox.ac.uk

Oxford University Computing Laboratory
Wolfson Building,
Parks Road,
Oxford, OX1 3QD, UK






The spectra and pseudospectra of nonsymmetric Toeplitz or circulant matrices with slowly varying coefficients are considered. Such matrices are characterized by a symbol that depends on both space and wave number. It is shown that when a certain twist condition is satisfied, analogous to Hormander's commutator condition for partial differential equations, epsilon-pseudoeigenvectors of such matrices for exponentially small values of epsilon exist in the form of localized wave packets. These results are a discrete analogue of similar results for differential operators discussed recently by E. B. Davies and M. Zworski.


EPSRC Gregynog Workshop, 21-26 July 2002

Gregynog Abstracts