Geodesic
Spectral asymptotic behavior of a class of integral operators
Matematičeskie zametki, Tome 16 (1974) no. 5, pp. 741-750 
A. A. Laptev. Spectral asymptotic behavior of a class of integral operators. Matematičeskie zametki, Tome 16 (1974) no. 5, pp. 741-750. http://geodesic.mathdoc.fr/item/MZM_1974_16_5_a7/
@article{MZM_1974_16_5_a7,
     author = {A. A. Laptev},
     title = {Spectral asymptotic behavior of a~class of integral operators},
     journal = {Matemati\v{c}eskie zametki},
     pages = {741--750},
     year = {1974},
     volume = {16},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1974_16_5_a7/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Integral operators of the type $$ (Tf)(x)=\int_0^1\frac{x^\beta y^\gamma}{(x+y)^\alpha}f(y)\,dy, $$ the kernels of which have a singularity at a single point, are discussed. H. Widom's method and some of his results are used to show that, if $\alpha>0$, $\beta,\gamma>-\frac12$, $\rho\stackrel{def}=\beta+\gamma-\alpha+1>0$, then we have for the distribution function of the singular numbers of the operator, $$ \lim_{\varepsilon\to0}N(\varepsilon,T)ln^{-2}\frac1\varepsilon=\frac1{2\pi^2\rho}. $$