Toeplitz matrices and determinants with Fisher-Hartwig symbols
نویسندگان
چکیده
منابع مشابه
TOEPLITZ MATRICES WITH FISHER - HARTWIG SYMBOLS 3 norm of a
We describe the asymptotics of the spectral norm of finite Toeplitz matrices generated by functions with Fisher-Hartwig singularities as the matrix dimension goes to infinity. In the case of positive generating functions, our result provides the asymptotics of the largest eigenvalue, which is of interest in time series with long-range memory.
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we call a the symbol of the sequence {Tn} and denote Tn by Tn(a). The case where a is in L∞(T) is easy, since then ‖Tn(a)‖ → ‖a‖∞ as n → ∞. Things are more complicated for a ∈ L(T) \L∞(T). We here focus our attention on so-called FisherHartwig symbols with a single singularity, that is, we consider functions a of the form a(t) = |t− t0|φβ,t0(t)b(t) (t ∈ T) where t0 ∈ T, α is a complex number su...
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With localization techniques one can obtain general limit theorems for Toeplitz determinants with Fisher-Hartwig singularities from the asymptotics for any symbol with one singularity of general type. There exists a family of these for which the determinants can be evaluated explicitly and their asymptotics determined. But for the Wiener-Hopf analogue, although there are likely analogous locali...
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The asymptotics of the Schatten norms of finite Toeplitz matrices generated by functions with a Fisher-Hartwig singularity are described as the matrix dimension n goes to infinity. The message of the paper is to reveal some kind of a kink: the pth Schatten norm increases as n to the power 1/p before the singularity reaches a critical point and as n to an exponent depending on the singularity be...
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The conjecture of Fisher and Hartwig, published in 1968, describes the asymptotic expansion of Toeplitz determinants with singular generating functions. For more than twenty years progress was made in extending the validity of the conjecture, but recent computer experiments led to counter-examples that show the limits of the original conjecture and pointed the way to a revised conjecture. This ...
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ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 1985
ISSN: 0022-1236
DOI: 10.1016/0022-1236(85)90085-0