This article is cited in 1 paper

On the nature of the spectrum of self-adjoint extensions of operators admitting separation of variables

V. A. Mikhailets

Institute of Mathematics, Ukrainian National Academy of Sciences

Abstract: We consider the operators: $L_0=\overline{M_0\otimes E''+E'\otimes Q}$, acting in the tensor product of the infinite-dimensional Hilbert spaces $H'$ and $H''$, where the operator $M_0$ is symmetric in $H'$ and $Q$ is self-adjoint in $H''$. We study the problem concerning the existence of self-adjoint extensions, the spectrum of which possesses certain preassigned properties. In particular, we obtain necessary and sufficient conditions under which the operator $L_0$ admits self-adjoint extensions with a discrete spectrum.

UDC: 517.9

Received: 12.02.1974

 English version: Mathematical Notes, 1974, 16:4, 936–939

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