Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asmptotic of the eigenvalues of Toeplitz matrices with even symbol   In this article we first obtain an asymptotic expression of the $N+1$
eigenvalues of the Toeplitz matrix $T_N(f)$ where $f$ is a strictly increasing
or strictly decreasing, differentiable and even function on $[-\pi,\pi]$. In
the particular case where the symbol only verifies these assumptions locally we
specify the eigenvalues that belong to a certain interval. In the case where
the symbol of the Toeplitz matrix is of the form $h_\alpha = (1-\cos
\theta)^{\alpha} c$ with $\alpha>\frac{1}{2}$ and $c$ a regular function we
give the general expression of the eigenvalues and a second order of this
asymptotic for a subset of the small eigenvalues as well as an approximation of
the eigenvectors.

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The categories of this paper are: cmp-lg
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The categories of this paper are: ao-sci
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The categories of this paper are: dg-ga
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: eess
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-th
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The categories of this paper are: econ
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The categories of this paper are: astro-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: gr-qc
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The categories of this paper are: q-alg
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The categories of this paper are: q-bio
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The categories of this paper are: chao-dyn
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The categories of this paper are: stat