Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Inversion des matrices de Toeplitz dont le symbole admet un z\'ero
  d'ordre fractionnaire positif, valeur propre minimale   Inversion of Toeplitz matrices with singular symbol. Minimal eigenvalues.
Three results are stated in this paper. The first one is devoted to the study
of the orthogonal polynomial with respect of the weight $\varphi_{\alpha}
(\theta)=\vert 1- e^{i \theta} \vert ^{2\alpha} f_{1}(e^{i \theta})$, with
$\alpha> \demi$ and $\alpha \in \rr \setminus \nn $, and $f_{1}$ a regular
function. We obtain an asymptotic expansion of the coefficients of these
polynomials, and we deduce an asymptotic of the entries of $\left( T_{N}
(\varphi_{\alpha})\right)^{-1}$ where $T_{N} (\varphi_{\alpha})$ is a Toeplitz
matrix with symbol $\varphi_{\alpha}$. Then we extend a result of A. B\"ottcher
and H. Widom result related to the minimal eigenvalue of the Toeplitz matrix
$T_{N}(\varphi_{\alpha})$. For $N$ goes to the infinity it is well known that
this minimal eigenvalue admit as asymptotic $\frac{c_{\alpha}}{N^{2\alpha}}
f_{1}(1)$. When $\alpha\in \nn$ the previous authors obtain an asymptotic of
$c_{\alpha}$ for $\alpha$ going to the infinity, and they have the bounds of
$c_{\alpha}$ for the other cases. Here we obtain the same type of results but
for $\alpha$ a positive real.

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The categories of this paper are: stat
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The categories of this paper are: q-bio
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The categories of this paper are: cond-mat
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The categories of this paper are: nlin
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The categories of this paper are: mtrl-th
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The categories of this paper are: eess
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The categories of this paper are: hep-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: physics
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The categories of this paper are: hep-ex
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The categories of this paper are: cs
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The categories of this paper are: q-alg
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The categories of this paper are: q-fin
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The categories of this paper are: astro-ph