Hermitian symplectic geometry and the Schr"{o}dinger operator on the graph

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dc.contributor.author Harmer, M. en
dc.date.accessioned 2009-08-28T03:20:44Z en
dc.date.available 2009-08-28T03:20:44Z en
dc.date.issued 2000 en
dc.identifier.citation Department of Mathematics - Research Reports-444 (2000) en
dc.identifier.issn 1173-0889 en
dc.identifier.uri http://hdl.handle.net/2292/4985 en
dc.description.abstract The theory of self-adjoint extensions is closely related to the theory of hermitian symplectic geometry cite{Pav,Kost:Sch,Nov3}. Here we develop this idea, showing that it may also be used to consider symmetric extensions of a symmetric operator. Furthermore we find an explicit parameterisation of the Lagrange Grassmannian in terms of the unitary matrices $U (n)$. This allows us to explicitly describe all self-adjoint boundary conditions for the Schr"{o}dinger operator on the graph in terms of a unitary matrix. We show that the asymptotics of the scattering matrix can be simply expressed in terms of this unitary matrix. \ Using the construction of the asymptotic hermitian symplectic space cite{Nov1,Nov3} we derive a formula for the scattering matrix of a graph in terms of the scattering matrices of its subgraphs. This also provides a characterisation of the discrete eigenvalues embedded in the continuous spectrum. en
dc.publisher Department of Mathematics, The University of Auckland, New Zealand en
dc.relation.ispartofseries Research Reports - Department of Mathematics en
dc.rights.uri https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm en
dc.source.uri http://www.math.auckland.ac.nz/Research/Reports/view.php?id=444 en
dc.title Hermitian symplectic geometry and the Schr"{o}dinger operator on the graph en
dc.type Technical Report en
dc.subject.marsden Fields of Research::230000 Mathematical Sciences::230100 Mathematics en
dc.rights.holder The author(s) en

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