Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Hilbert $L$-matrix   We analyze spectral properties of the Hilbert $L$-matrix
$$\left(\frac{1}{\max(m,n)+\nu}\right)_{m,n=0}^{\infty}$$ regarded as an
operator $L_{\nu}$ acting on $\ell^{2}(\mathbb{N}_{0})$, for
$\nu\in\mathbb{R}$, $\nu\neq0,-1,-2,\dots$. The approach is based on a spectral
analysis of the inverse of $L_{\nu}$, which is an unbounded Jacobi operator
whose spectral properties are deducible in terms of the unit argument
${}_{3}F_{2}$-hypergeometric functions. In particular, we give answers to two
open problems concerning the operator norm of $L_{\nu}$ published by L. Bouthat
and J. Mashreghi in [Oper. Matrices 15, No. 1 (2021), 47--58]. In addition,
several general aspects concerning the definition of an $L$-operator, its
positivity, and Fredholm determinants are also discussed.

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The categories of this paper are: hep-lat
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The categories of this paper are: cmp-lg
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The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
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The categories of this paper are: mtrl-th
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The categories of this paper are: nlin
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The categories of this paper are: eess
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The categories of this paper are: chao-dyn
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The categories of this paper are: ao-sci
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The categories of this paper are: q-alg
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The categories of this paper are: chem-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: econ
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The categories of this paper are: hep-th