Indefinite Boundary Eigenvalue Problems in a Pontrjagin Space Setting |
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Authors: | Albert Schneider Rolf Vonhoff |
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Institution: | 1. Universit?t Dortmund Fachbereich Mathematik, 44221, Dortmund, Germany
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Abstract: | We study eigenvalue problems Fy = λ Gy consisting of Hamiltonian systems of ordinary differential equations on a compact interval with symmetric λ-linear boundary conditions. The problems we are interested in are non-definite: neither left-nor right-definite. Instead of this, we give some weak condition on one coefficient of the Hamiltonian system which ensures that a hermitian form associated with the operator F has at most finitely many negative squares. This enables us to study the problem by the help of a compact self-adjoint operator in a Pontrjagin space and we obtain as a main result uniformly convergent eigenfunction expansions. In the final section, applications to formally self-adjoint differential equations of higher order are given. |
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