This article is cited in 2 papers

On the essential and the discrete spectra of a Fredholm type partial integral operator

G. P. Arzikulov^a, Yu. Kh. Eshkabilov<sup>b

a</sup> Tashkent State Technical University, Tashkent, Uzbekistan
^b Faculty of Mathematics and Mechanics, Ulugbek National University of Uzbekistan, Tashkent, Uzbekistan

Abstract: We investigate the structure of the essential spectrum of a self-adjoint Fredholm type partial integral operator $H$. We obtain an explicit description of the essential spectrum of $H$ and prove that an eigenvalue of $H$ exists.

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

UDC: 517.984.53

Received: 10.02.2014

 English version: Siberian Advances in Mathematics, 2015, 25:4, 231–242

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