The spectrum of a polyharmonic operator in domains with noncompact boundaries (Q1425491)

The author establishes a sufficient condition of continuity for spectrum of the operator \[ L = (-\Delta)^m\: L_2(\Omega)\to L_2(\Omega),\qquad \Delta = \sum\limits_{i=1}^n \frac{\partial^2}{\partial x_i^2},\qquad m=1,2,..., \] with the domain of definition \[ D(L) = \big\{u\: u\in \overset\circ W_2^m(\Omega),\, \Delta^mu\in L_2(\Omega)\big\} \] in the case when the domain \(\Omega\) possesses noncompact boundary.