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Inverse spectral results on even dimensional tori

Carolyn S. GordonPierre GueriniThomas KappelerDavid L. Webb — 2008

Annales de l’institut Fourier

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 S p e c ( 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 S p e c ( Q ; L , ) determines the potential Q . With a genericity condition, we show that if the connection is invariant under...

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