On the inverse scattering problem on branching graphs

By Pavel Kurasov, F. Stenberg. 2002

243 citations recorded by the source corpus.

Subfields: Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/f97cfe70f2302ebaee4fa549c2ef5fd1d7ad6582

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In Mathematical Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Graph models for waves in thin structures (2002, methodology): “The reader can find the up to date survey of the available results in [126].”
Inverse spectral problem for quantum graphs (2006, background): “More precisely this equivalence is described in [3, 27].”
Graph Laplacians and topology (2008, background): “3) In [20] and [4] it was shown that the knowledge of the scattering matrix is not sufficient to reconstruct the Euler characteristic of the graphs, but it appears that”
Homogeneous trees of second order Sturm-Liouville equations: A general theory and program (2008, background): “It is known that in general this is impossible (see [23, 33, 153]).”
Schrödinger operators on graphs and geometry I: Essentially bounded potentials (2008, unknown): “Nowaczyk [6,24–26,30,31].”
Rayleigh estimates for differential operators on graphs (2014, background): “More about how to define general quantum graphs and the description of their spectral and transmission properties can be found in [19] and [26], and recent surveys [3], [22], and [23].”
Quantum graphs: I. Some basic structures (2004, unknown): “[3, 5, 6, 7, 8], [16]-[20], [29]-[32], [39], [43]-[49], [54]-[61], [64, 65, 74, 79, 80], other”
Recent progress in the boundary control method (2007, unknown): “For other approaches and results see [3, 73, 97].”
Inverse problem for the Sturm–Liouville equation on a star‐shaped graph (2007, background): “The answer in these papers is negative or positive depending on the approach (see also [19]).”
Boundary spectral inverse problem on a class of graphs (trees) by the BC method (2004, background): “However, a direct analogue of the classical statement would be to recover ρ on a given (see [12, 14, 17]).”