Certain classes of extension of a lacunary Hermitian operator

Certain classes of extensions of a lacunary Hermitian operator are described in terms of abstract boundary conditions. The connection between the asymptotic behavior of eigenvalues of an extension near the boundary of lacuna and the asymptotic of the negative spectrum of the corresponding boundary operator is found.Candidate of Phisicomathematical Science.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 2, pp. 215–233, February, 1992.