Hamiltonian Systems with Eigenvalue Depending Boundary Conditions View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

1988

AUTHORS

Aad Dijksma , Heinz Langer , Henk de Snoo

ABSTRACT

In 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... »

PAGES

37-83

References to SciGraph publications

Book

TITLE

Contributions to Operator Theory and its Applications

ISBN

978-3-0348-9978-9
978-3-0348-9284-1

Author Affiliations

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-3-0348-9284-1_3

DOI

http://dx.doi.org/10.1007/978-3-0348-9284-1_3

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