@article{Reconstruction:2024,
      recid = {2024},
      author = {Campos Salas, Daniel},
      title = {Reconstruction of the Magnetic Field for a Schrödinger  Operator in a Cylindrical Setting},
      publisher = {The University of Chicago},
      school = {Ph.D.},
      address = {2019-08},
      pages = {125},
      abstract = {In this thesis we consider a magnetic Schrödinger inverse  problem over a compact domain contained in an infinite  cylindrical manifold. We show that, under certain  conditions on the electromagnetic potentials, we can  recover the magnetic field from boundary measurements in a  constructive way. A fundamental tool for this procedure is  a global Carleman estimate for the magnetic Schrödinger  operator. We prove this by conjugating the magnetic  operator essentially into the Laplacian, and using the  Carleman estimates for it proven by Kenig--Salo--Uhlmann in  the anisotropic setting, see [KSU11a]. The conjugation is  achieved through pseudodifferential operators over the  cylinder, for which we develop the necessary results.

The  main motivations to attempt this question are the following  results concerning the magnetic Schrödinger operator:  first, the solution to the uniqueness problem in the  cylindrical setting in [DSFKSU09], and, second, the  reconstruction algorithm in the Euclidean setting from  [Sal06]. We will also borrow ideas from the reconstruction  of the electric potential in the cylindrical setting from  [KSU11b]. These two new results answer partially the  Carleman estimate problem (Question 4.3.) proposed in  [Sal13] and the reconstruction for the magnetic Schrödinger  operator mentioned in the introduction of [KSU11b]. To our  knowledge, these are the first global Carleman estimates  and reconstruction procedure for the magnetic Schrödinger  operator available in the cylindrical setting.},
      url = {http://knowledge.uchicago.edu/record/2024},
      doi = {https://doi.org/10.6082/uchicago.2024},
}