INVESTIGATION OF THE SPECTRUM AND RESOLVENT OF A FOURTH-ORDER DIFFERENTIAL SHEAF WITH A TRIPLE CHARACTERISTIC ROOT

Author(s):  E.G. Orudzhev, Dr., Baku State University, Baku, Republic of Azerbaijan, elsharorucov63@mail.ru

S.A. Aliev, Nakhchivan Teachers Institute, Nakhchivan, Republic of Azerbaijan, sahil.liyev83@mail.ru

Issue:  Volume 51, № 1

Rubric:  Mathematics

Annotation:  The article is considered that, the spectrum and the resolvent of a structure of fourth-order differential operators are investigated in space 0; 2 L , when one triple root is the main characteristic 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 a bounded integral operator, defined on the whole space 0; 2 L , with a Carleman type kernel.

Keywords:  spectrum, eigen function, resolvent, adjoint operator, Carleman type kernel

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