Inverse Problems for Graph Laplacians
(2008) Abstract
 This thesis is devoted to inverse spectral problems for Laplace operators on metric graphs, and it is based on the following papers:
Paper I  P. Kurasov and M. Nowaczyk 2005 Inverse spectral problem for quantum graphs J. Phys. A: Math. Gen 38 490115
Paper II  M. Nowaczyk 2007 Inverse spectral problem for quantum graphs with rationally dependent edges Operator Theory, Analysis and Mathematical Physics Operator Theory: Advances and Applications 147 10516
Paper III  P. Kurasov and M. Nowaczyk 2007 Geometric properties of quantum graphs and vertex scattering matrices, Preprint 2007:21 Centre for Mathematical Sciences, Lund University.
Paper IV  S. Avdonin, P. Kurasov and M. Nowaczyk 2007 On the... (More)  This thesis is devoted to inverse spectral problems for Laplace operators on metric graphs, and it is based on the following papers:
Paper I  P. Kurasov and M. Nowaczyk 2005 Inverse spectral problem for quantum graphs J. Phys. A: Math. Gen 38 490115
Paper II  M. Nowaczyk 2007 Inverse spectral problem for quantum graphs with rationally dependent edges Operator Theory, Analysis and Mathematical Physics Operator Theory: Advances and Applications 147 10516
Paper III  P. Kurasov and M. Nowaczyk 2007 Geometric properties of quantum graphs and vertex scattering matrices, Preprint 2007:21 Centre for Mathematical Sciences, Lund University.
Paper IV  S. Avdonin, P. Kurasov and M. Nowaczyk 2007 On the Reconstruction of the Boundary Conditions for Star Graphs, Preprint 2007:29 Centre for Mathematical Sciences, Lund University.
In the first paper, we prove the trace formula and show that it can be used to reconstruct the metric graph in the case of rationally independent lengths of the edges and the Laplace operator with standard boundary conditions at the vertices. The second paper generalises this result by showing that the condition of rational independence of lengths of the edges can be weakened. In the third paper the possibility to parameterise vertex boundary conditions via the scattering matrix is investigated. The trace formula is generalised to include even arbitrary vertex boundary conditions leading to energy independent vertex scattering matrices, socalled nonresonant boundary conditions. In the last paper, we turn to the problem of recovering boundary conditions and solve it for the special case of the star graph. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/792090
 author
 Nowaczyk, Marlena ^{LU}
 supervisor

 Pavel Kurasov ^{LU}
 opponent

 Professor Marletta, Marco, Cardiff, Storbritannien
 organization
 publishing date
 2008
 type
 Thesis
 publication status
 published
 subject
 keywords
 Spectral theory, Laplace operator, Trace formula, Quantum graphs
 pages
 104 pages
 publisher
 Marlena Nowaczyk
 defense location
 Room MH:C, Matematikcentrum, SÃ¶lvegatan 18, Lund University Faculty of Engineering.
 defense date
 20080122 10:15
 external identifiers

 other:LUTFMA10272007
 ISSN
 14040034
 ISBN
 9789162873646
 language
 English
 LU publication?
 yes
 id
 9b8de254139245a6bfbc1ba44ba301af (old id 792090)
 date added to LUP
 20071221 15:17:54
 date last changed
 20160919 08:44:47
@phdthesis{9b8de254139245a6bfbc1ba44ba301af, abstract = {This thesis is devoted to inverse spectral problems for Laplace operators on metric graphs, and it is based on the following papers:<br/><br> Paper I  P. Kurasov and M. Nowaczyk 2005 Inverse spectral problem for quantum graphs J. Phys. A: Math. Gen 38 490115<br/><br> Paper II  M. Nowaczyk 2007 Inverse spectral problem for quantum graphs with rationally dependent edges Operator Theory, Analysis and Mathematical Physics Operator Theory: Advances and Applications 147 10516<br/><br> Paper III  P. Kurasov and M. Nowaczyk 2007 Geometric properties of quantum graphs and vertex scattering matrices, Preprint 2007:21 Centre for Mathematical Sciences, Lund University.<br/><br> Paper IV  S. Avdonin, P. Kurasov and M. Nowaczyk 2007 On the Reconstruction of the Boundary Conditions for Star Graphs, Preprint 2007:29 Centre for Mathematical Sciences, Lund University.<br/><br> In the first paper, we prove the trace formula and show that it can be used to reconstruct the metric graph in the case of rationally independent lengths of the edges and the Laplace operator with standard boundary conditions at the vertices. The second paper generalises this result by showing that the condition of rational independence of lengths of the edges can be weakened. In the third paper the possibility to parameterise vertex boundary conditions via the scattering matrix is investigated. The trace formula is generalised to include even arbitrary vertex boundary conditions leading to energy independent vertex scattering matrices, socalled nonresonant boundary conditions. In the last paper, we turn to the problem of recovering boundary conditions and solve it for the special case of the star graph.}, author = {Nowaczyk, Marlena}, isbn = {9789162873646}, issn = {14040034}, keyword = {Spectral theory,Laplace operator,Trace formula,Quantum graphs}, language = {eng}, pages = {104}, publisher = {Marlena Nowaczyk}, school = {Lund University}, title = {Inverse Problems for Graph Laplacians}, year = {2008}, }