An expansion theorem for regular elliptic eigenvalue problem with eigenvalue parameter in the boundary conditions

The object of this paper is to establish the expansion theorem for a regular elliptic eigenvalue problem of a general multiply connected bounded domain in R^m, (m>=2), where the eigenvalue parameter @l is contained in the elliptic partial differential equation and in the general type of boundary conditions. We associated with this problem an essentially self-adjoint operator A in a suitably defined Hilbert space H and then we develop an associated eigenfunction expansion theorem.

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