dc.contributor.author |
Melnikov, Y. |
en |
dc.contributor.author |
Pavlov, B. |
en |
dc.date.accessioned |
2009-08-28T03:20:48Z |
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dc.date.available |
2009-08-28T03:20:48Z |
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dc.date.issued |
2000 |
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dc.identifier.citation |
Department of Mathematics - Research Reports-439 (2000) |
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dc.identifier.issn |
1173-0889 |
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dc.identifier.uri |
http://hdl.handle.net/2292/4990 |
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dc.description.abstract |
In actual paper we develop the spectral analysis of Schr"odinger operators on lattice type graphs. For basic example of qubic periodic graph the problem is reduced to the spectral analysis of the regular differential operators on a fundamental star-like subgraph with a selfadjoint condition at the central node and quasiperiodic conditions at the boundary vertices. Using an explicite expression for resolvent of lattice-type operator we develop in the second sections the Lippmann- Schwinger techniques for the perturbed periodic operator and construct the corresponding scattering matrix. It serves as a base for the approximation of the multy-dimensional Schr"odinger operator by the onedimansional operator on graph : in the third section of the paper for given $N$-dimensional Schr"odinger operators with rapidly decreasing potential we construct a lattice-type operator on cubic graph embedded into ${bf R}^N$ and show that the original $N$-dimensional scattering problem can be approximated in proper sense by the corresponding scattering problem for the perturbed lattice operator. |
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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=439 |
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dc.title |
Scattering on graphs and one-dimensional approximation of $N-$dimensional Schr"odinger operators |
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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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