Geodesic
On the number of negative eigenvalues of a~partial integral operator
Matematičeskie trudy, Tome 17 (2014) no. 1, pp. 128-144

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We find the lower boundary for the essential spectrum of a Fredholm type partial integral operator $H$. We also obtain an estimate for the number of eigenvalues below this boundary. 
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R. R. Kucharov; Yu. Kh. Eshkabilov. On the number of negative eigenvalues of a~partial integral operator. Matematičeskie trudy, Tome 17 (2014) no. 1, pp. 128-144. http://geodesic.mathdoc.fr/item/MT_2014_17_1_a5/