This article is cited in 1 paper

On the number of negative eigenvalues of a partial integral operator

R. R. Kucharov, Yu. Kh. Eshkabilov

National University of Uzbekistan named after M. Ulugbek, Faculty of Mathematics and Mechanics, Tashkent, Uzbekistan

Abstract: 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.

Key words: essential spectrum, discrete spectrum, the lower boundary of the essential spectrum, Fredholm type partial integral operator.

UDC: 517.984.53

Received: 14.05.2013

 English version: Siberian Advances in Mathematics, 2015, 25:3, 179–190

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