We consider the Schrödinger operator L = −d2 /dx 2 +q on the interval [0,1] depending on an L 2-potential q and endowed with periodic or anti-periodic boundary conditions. We prove results about correspondencies between the asymptotic behaviour of the spectral gaps of L and the regularity of q in the Gevrey case, among others. The proofs are based on a Fourier block decomposition due to Kappeler &Mityagin, and a novel application of the implicit function theorem.
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Pöschel, J. (2008). Spectral gaps of potentials in weighted Sobolev spaces. In: Craig, W. (eds) Hamiltonian Dynamical Systems and Applications. NATO Science for Peace and Security Series. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-6964-2_17
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DOI: https://doi.org/10.1007/978-1-4020-6964-2_17
Publisher Name: Springer, Dordrecht
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