Investigation of the spectrum and resolvent of a fourth-order differential sheaf with a triple characteristic root

The article is considered that, the spectrum and the resolvent of a structure of fourth-orderdifferential operators are investigated in space $L_2(0; \infty)$, when one triple root is the maincharacteristic polynomial . It is shown that, a sheaf can have a finite or countable number of eigenvalues in the open lower and open upper half-planes, and the continuous spectrum fills the all real axis, where spectral singularities are located. It is proved that, the sheaf resolvent is abounded integral operator, defined on the whole space $L_2(0; \infty)$, with a Carleman type kernel.