Abstract
Questions in probability and statistical physics lead to the problem of finding the eigenvectors associated with the extreme eigenvalues of Toeplitz matrices generated by Fisher-Hartwig symbols. We here simplify the problem and consider pseudomodes instead of eigenvectors. This replacement allows us to treat fairly general symbols, which are far beyond Fisher-Hartwig symbols. Our main result delivers a variety of concrete unit vectors xn such that if Tn(a) is the n × n truncation of the infinite Toeplitz matrix generated by a function a ∈ L1 satisfying mild additional conditions and λ is in the range of this function, then ‖Tn(a)xn − λxn‖ → 0 . Mathematics subject classification (2000): 47B35, 15A18, 41A80, 46N30.
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