Asymptotics of Toeplitz, Hankel, and Toeplitz+Hankel determinants with Fisher-Hartwig singularities
نویسندگان
چکیده
منابع مشابه
Schatten norms of Toeplitz matrices with Fisher-Hartwig singularities
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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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.
متن کاملNorms of Toeplitz Matrices with Fisher-Hartwig Symbols
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...
متن کاملON THE ASYMPTOTICS OF SOME LARGE HANKEL DETERMINANTS GENERATED BY FISHER-HARTWIG SYMBOLS DEFINED ON THE REAL LINE By
We investigate the asymptotics of Hankel determinants of the form
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ژورنال
عنوان ژورنال: Annals of Mathematics
سال: 2011
ISSN: 0003-486X
DOI: 10.4007/annals.2011.174.2.12