NANOSYSTEMS: PHYSICS, CHEMISTRY, MATHEMATICS, 2013, 4 (4), P. 529–537
EFIMOV’S EFFECT FOR PARTIAL INTEGRAL OPERATORS OF FREDHOLM TYPE
Yu. Kh. Eshkabilov – Department of Mechanics and Mathematics, National University of Uzbekistan, Tashkent, Uzbekistan; yusup62@mail.ru
R. R. Kucharov – Department of Mechanics and Mathematics, National University of Uzbekistan, Tashkent, Uzbekistan; ramz3364647@yahoo.com
We study the existence of an infinite number of eigenvalues (the existence of Efimov’s effect) for a self-adjoint partial integral operators. We prove a theorem on the necessary and sufficient conditions for the existence of Efimov’s effect for the Fredholm type partial integral operators.
Keywords: essential spectrum, discrete spectrum, Efimov’s effect, partial integral operator.
PACS 02.30.Tb
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