An expansion theorem for an eigenvalue problem of an arbitrary multiply connected domain with an eigenparameter in a general type of boundary conditions |
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Authors: | E M E Zayed S F M Ibrahim |
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Institution: | (1) Mathematics Department Faculty of Science, Zagazig University, Zagazig, Egypt;(2) Mathematics Department Faculty of Science, Ain Shams University, Heliopolis, Cairo, Egypt |
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Abstract: | The object of this paper is to establish an expansion theorem for a regular right-definite eigenvalue problem with an eigenvalue parameter 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 inR
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(n2). 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. |
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Keywords: | Eigenvalue problem Multiply connected domain Eigenfunction expansion |
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