dc.contributor.author |
Harmer, M. |
en |
dc.date.accessioned |
2009-08-28T03:20:44Z |
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dc.date.available |
2009-08-28T03:20:44Z |
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dc.date.issued |
2000 |
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dc.identifier.citation |
Department of Mathematics - Research Reports-444 (2000) |
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dc.identifier.issn |
1173-0889 |
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dc.identifier.uri |
http://hdl.handle.net/2292/4985 |
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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. |
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dc.publisher |
Department of Mathematics, The University of Auckland, New Zealand |
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dc.relation.ispartofseries |
Research Reports - Department of Mathematics |
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dc.rights.uri |
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm |
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dc.source.uri |
http://www.math.auckland.ac.nz/Research/Reports/view.php?id=444 |
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dc.title |
Hermitian symplectic geometry and the Schr"{o}dinger operator on the graph |
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dc.type |
Technical Report |
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dc.subject.marsden |
Fields of Research::230000 Mathematical Sciences::230100 Mathematics |
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dc.rights.holder |
The author(s) |
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