Isospectral periodic Torii in dimension 2
Annales de l'I.H.P. Analyse non linéaire, Volume 32 (2015) no. 6, pp. 1173-1188.

We consider two dimensional real-valued analytic potentials for the Schrödinger equation which are periodic over a lattice 𝕃. Under certain assumptions on the form of the potential and the lattice 𝕃, we can show there is a large class of analytic potentials which are Floquet rigid and dense in the set of C ( 2 /𝕃) potentials. The result extends the work of Eskin et al., in “On isospectral periodic potentials in n , II.”

Nous considérons les potentiels analytiques à valeurs réelles en dimension deux pour l'equation de Schrödinger qui sont périodiques sur un réseau 𝕃. Sous certaines hypothèses sur la forme du potentiel et du réseau 𝕃, nous montrons qu' il y a une grande classe de potentiels analytiques Floquet rigides et denses dans l'ensemble de C ( 2 /𝕃) potentiels. Ce résultat prolonge le travail de Eskin et al., dans “Les potentiels périodiques isospectraux dans n , II.”

DOI: 10.1016/j.anihpc.2014.06.001
Classification: 35J10,  35P05,  65M32
Keywords: Inverse problems, Spectral theory, Schrödinger equations
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     title = {Isospectral periodic {Torii} in dimension 2},
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Waters, Alden. Isospectral periodic Torii in dimension 2. Annales de l'I.H.P. Analyse non linéaire, Volume 32 (2015) no. 6, pp. 1173-1188. doi : 10.1016/j.anihpc.2014.06.001. http://archive.numdam.org/articles/10.1016/j.anihpc.2014.06.001/

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