Boundary spectral inverse problem on a class of graphs (trees) by the BC method
By Mikhail I. Belishev. 2004
167 citations recorded by the source corpus.
Subfields: Control and Systems Engineering, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/61365cd29c265b5d267b7a573698b4ae0780c03d
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Control and Systems Engineering
- Pavel Kurasov
- Vjacheslav A. Yurko
- Peter Kuchment
- A. Vakulenko
- Mikhail I. Belishev
- Matti Lassas
- Lauri Oksanen
In Mathematical Physics
- Peter Kuchment
- Pavel Kurasov
- Mikhail I. Belishev
- Vjacheslav A. Yurko
- A. Vakulenko
- Sergey A. Buterin
- Natalia Pavlovna Bondarenko
- Chuan-Fu Yang
Citations in the corpus
- Inverse spectral problems for Sturm–Liouville operators on graphs (2005, background): “But unfortunately the formulation of the inverse problem in [ 22 ] is overdetermined (even in the simplest case of the classical Sturm–Liouville operator on an interval), and the question of how to formulate the inverse problem correctly remains open.”
- Schrödinger operators on graphs and geometry I: Essentially bounded potentials (2008, background): “It is possible to state that this problem is fully understood now [1,3,4,9,27,34,36,37].”
- Inverse problems on graphs: recovering the tree of strings by the BC-method (2006, background): “Note in conclusion that there exists a series of inverse problems on trees (for the wave, heat and other equations: see [2]) which can be reduced to the spectral inverse problem and, therefore, can be solved by our technique.”
- Homogeneous trees of second order Sturm-Liouville equations: A general theory and program (2008, background): “See also [17, 18, 45, 97, 152, 187, 214] for the control theory approach and other discussions of the inverse problem.”
- Graph Laplacians and topology (2008, background): “It has been proven by different authors that in the case of finite metric trees, the graphs and the potentials can be reconstructed from the corresponding scattering matrix or certain spectral data [1], [2], [7] and [29].”
- Recent progress in the boundary control method (2007, background): “As is shown in [26], the equality ( opt, ρ ′ opt) = ( ′′ opt, ρ ′′ opt) holds iff the trees are spatially isometric, i.”