On Magnetic Boundary Control for Metric Graphs
Main Article Content
Abstract
It is investigated how magnetic boundary control can be used to solve inverse problems for Schrödinger operators on metric graphs. Explicit examples show that such reconstruction is sometimes possible, starting from a single contact vertex in the graph.
Article Details
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
S. Avdonin, V. Mikhaylov, A. Rybkin, Comm. Math. Phys. 275, 791 (2007)
M.I. Belishev, Inverse Probl. 13, R1 (1997)
M I Belishev, Inverse Probl. 23, R1 (2007)
M.I. Belishev, J. Math. Sci. 155, 343 (2008)
M.I. Belishev, in: Dynamical Inverse Problems: Theory and Application, Vol. 529, Springer Vienna, 2011, p. 85
A. Rybkin, Inverse Probl. Imaging 3, 139 (2009)
G. Berkolaiko, P. Kuchment, Introduction to Quantum Graphs, Mathematical Surveys and Monographs, Vol. 186, American Mathematical Society, Providence (RI) 2013
P. Kurasov, Spectral Geometry of Graphs, Operator Theory Advances and Applications, Birkhäuser/Springer, 2023
R. Band, G. Berkolaiko, C.H. Joyner, Wen Liu, arXiv:1711.00918 (2017)
R. Band, O. Parzanchevski, G. Ben-Shach, J. Phys. A 42, 175202 (2009)
J. Boman, P. Kurasov, Adv. Appl. Math. 35, 58 (2005)
A. Chernyshenko, V. Pivovarchik, Integral Equ. Oper. Theory 92, 17 (2020)
J. Stewart Fabila-Carrasco, F. Lledó, O. Post, Anal. Math. Phys. 13, 44 (2023)
B. Gutkin, U. Smilansky, J. Phys. A 34, 6061 (2001)
P. Kurasov, J. Muller, St. Petersburg Math. J. 35, 55 (2023)
P. Kurasov, M. Nowaczyk, J. Phys. A 38, 4901 (2005)
P. Kurasov, F. Stenberg, J. Phys. A 35, 101 (2002)
M.-E. Pistol, arXiv:2104.12885v4 (2022)
R. Brooks, Ann. Inst. Fourier 49, 707 (1999)
S. Butler, J. Grout, Electron. J. Combin. 18, 231 (2011)
W.H. Haemers, E. Spence, Eur. J. Comb. 25, 199 (2004)
L. Halbeisen, N. Hungerbühler, J. Graph Theory 31, 255 (1999)
J.J. Seidel, Proc. K. Ned. Akad. Wet. Ser. A: Math. Sci. 70, 188 (1967)
P. Kurasov, Math. Proc. Cambridge Philos. Soc. 148, 331 (2010)
S. Avdonin, P. Kurasov, Inverse Probl. Imaging 2, 1 (2008)
S Avdonin, P. Kurasov, M. Nowaczyk, Inverse Probl. Imaging 4, 579 (2010)
P. Kurasov, J. Math. Phys. 54, 042103 (2013)
H. Weyl, Math. Ann. 68, 220 (1910)
P. Kurasov, S. Naboko, Studia Math. 255, 303 (2020)
P. Kurasov, Acta Phys. Pol. A 132, 1666 (2017)
P. Kurasov, S. Naboko, ``M-functions and Eigenfunctions'', 2023
S. Albeverio, P. Kurasov, Singular Perturbations of Differential Operators, London Mathematical Society Lecture Note Series, Vol. 271, Cambridge University Press, Cambridge 2000