Geodesic
Asymptote of the eigenvalues of a~completely continuous operator
Matematičeskie zametki, Tome 14 (1973) no. 4, pp. 487-492.

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It is proved that if $\varphi(x)$ is the majorant of the $s$-numbers of a completely continuous operator $A$ (i.e., $\varphi'(x)\le0$, $s_n(A)\le\varphi(n)$) and if there are found numbers $\rho\in[0,1]$ and $r_0>0$ such that $r^\rho\varphi'(r)/\varphi(r)$ will be monotonic in $(r_0,\infty)$, then for some $\alpha>0$, $\varphi(\alpha x)$ will be a majorant of the eigenvalues of $A$. 
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     author = {K. Kh. Boimatov},
     title = {Asymptote of the eigenvalues of a~completely continuous operator},
     journal = {Matemati\v{c}eskie zametki},
     pages = {487--492},
     publisher = {mathdoc},
     volume = {14},
     number = {4},
     year = {1973},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1973_14_4_a3/}
}
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K. Kh. Boimatov. Asymptote of the eigenvalues of a~completely continuous operator. Matematičeskie zametki, Tome 14 (1973) no. 4, pp. 487-492. http://geodesic.mathdoc.fr/item/MZM_1973_14_4_a3/