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Inverse Spectral Results On Even Dimensional Tori, Carolyn Gordon, Pierre Guerini, Thomas Kappeler, David Webb
Inverse Spectral Results On Even Dimensional Tori, Carolyn Gordon, Pierre Guerini, Thomas Kappeler, David Webb
Dartmouth Scholarship
Given a Hermitian line bundle L over a flat torus M, a connection ∇ on L, and a function Q on M, one associates a Schrödinger operator acting on sections of L; its spectrum is denoted Spec(Q;L,∇). Motivated by work of V. Guillemin in dimension two, we consider line bundles over tori of arbitrary even dimension with “translation invariant” connections ∇, and we address the extent to which the spectrum Spec(Q;L,∇) determines the potential Q. With a genericity condition, we show that if the connection is invariant under the isometry of M defined by the map x→-x, then the spectrum …