Asymptotic behavior of the spectrum of integral operators with a singularity on the diagonal

In this paper the asymptotic behavior is studied of the spectrum of “weighted” integral operators of the form
$$ (\mathbf Tu)(y)=\int_{\mathbf R^m}b(y)T(x,y)\overline a(x)u(x)\,dx, $$
acting in the space $L_2(\mathbf R^m)$.
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