Ontology type: schema:Chapter
1988
AUTHORSAad Dijksma , Heinz Langer , Henk de Snoo
ABSTRACTIn earlier papers [DLS1–6] we have described the selfadjoint extensions, in indefinite inner product spaces and with nonempty resolvent sets of a symmetric closed relation S in a Hilbert space ℌ by means of generalized resolvents, characteristic functions and Štraus extensions. In this paper we show how these results can be applied when S comes from a 2n×2n Hamiltonian system of ordinary differential equations on an interval [a, b), (1.1) Jy′(t) = (ℓΔ(t) + H(t)) y(t) + Δ(t)f(t), t ∈[a, b), ℓ∈ℂ, which is regular in a and in the limit point case in b; for further specifications see Section 5. We pay special attention to selfadjoint extensions beyond the given space ℌ, as they give rise to eigenvalue and boundary value problems with boundary conditions of the form (1.2) A(ℓ)y1 (a) + B(ℓ)y 2 (a) = 0, in which the matrix coefficients A(ℓ) and В(ℓ) depend holomorphically on the eigenvalue parameter ℓ, see Theorem 7.1 below. The eigenvalue problem for such a selfadjoint extension in a larger space can be considered as a linearization of the corresponding boundary value problem (1.1) and (1.2). More... »
PAGES37-83
Contributions to Operator Theory and its Applications
ISBN
978-3-0348-9978-9
978-3-0348-9284-1
http://scigraph.springernature.com/pub.10.1007/978-3-0348-9284-1_3
DOIhttp://dx.doi.org/10.1007/978-3-0348-9284-1_3
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