О базисности системы собственных элементов в задачах сопряжения

In the work a spectral problem for a two-parametrical operator pencil $L(\lambda, \mu) := I + \lambda A− \mu B$, acting in a separable Hilbert space $H$, with operator factors $A, B, 0 < A \in \sigma_{\infty}, 0 \leq B \in \sigma_{\infty}$, and $\lambda$, $\mu$ $\in$ $\mathbb{R}$ is studied. There are considered cases when one parameter is fixed and the second is spectral. The given problem arises in studying of transmission problems on the base of the operator approach using auxiliary operators for elliptic boundary problems. This problem for a case $\lambda$, $\mu$ $\in$ $\mathbb{C}$ $\setminus$ $\mathbb{R}$ has been investigated earlier by the author. $\textit{The purpose of the given work}$ is to study the case of real values of parameters.

UDC:
517.98