An Expansion Theorem for an Eigenvalue Problem of an Arbitrary Multiply Connected Domain with an Eigenparameter in a General Type of Boundary Conditions

The object of this paper is to establish an expansion theorem for a regular right- definite eigenvalue problem with an eigenvalue parameter à which is contained in the Schrödinger partial differential equation and in a general type of boundary conditions on the boundary of an arbitrary multiply connected bounded domain in R(n> 2). We associate with this problem an essentially self-adjoint operator in a suitably defined Hilbert space and then we develop an associated eigenfunction expansion theorem.