T. Bouhennache, Point spectrum of elliptic operators in fibered half-cylinders and the related completeness problem, INTEG EQ OP, 39(2), 2001, pp. 182-192
We consider an elliptic system in a half-cylinder IR+ x omega with coeffici
ents constant in the direction of the axis and not necessarily smooth. We t
ake different boundary conditions on IR+ x partial derivative omega and Dir
ichlet condition on (0) x omega. This defines a self-adjoint operator A(D).
The main result in this paper is that AD does not have eigenvalues. This a
nswers conjecture 1.6 raised in [3]. When omega is bounded, we use this res
ult to prove the completeness of a part of the family of eigenvectors, and
associated vectors, of a corresponding operator pencils.