The structurally stable linear systems on the half-line are those with exponential dichotomies |
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Authors: | Kenneth J Palmer |
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Affiliation: | Department of Mathematics, Institute of Advanced Studies, Australian National University, Canberra, ACT, Australia |
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Abstract: | Let A be a selft-adjoint operator on the Hilbert space L2Ω, ?) = {u ε Lloc2(Ω)|∫Ω|2 ?(x)dx < + ∞} defined by means of a closed, semibounded, sesquilinear form a(·, ·). We obtain a necessary and sufficuents condition for the spectrum of A to be discrete. We apply this result to a Sturm-Liouville problem for an elliptic operator with discontinuous coefficients defined on an unbounded domain and to the study of the spectrum of a Hamiltonian defined by a pseudodifferential operator. |
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