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Статья

Inverse spectral theory for perturbed torus

Journal of Geometric Analysis. 2020. Vol. 30. P. 4427-4452.
Isozaki H., Korotyaev Evgeny.

We consider an inverse problem for Laplacians on rotationally
symmetric  manifolds, which are finite  for the transversal
direction and periodic with respect to the axis of the manifold,
i.e.,  Laplacians on tori.  We construct an infinite dimensional
analytic isomorphism between the space of profiles  (the radius of
the rotation) of the torus and the spectral data as well as the
stability estimates: those for the spectral data in terms of the
profile and conversely, for the profile in term of the spectral
data.