The Absolutely Continuous Spectrum in One Dimension

@inproceedings{Deift1983TheAC,
  title={The Absolutely Continuous Spectrum in One Dimension},
  author={Percy Deift and Beno{\^i}t Simon},
  year={1983}
}
We discuss the absolutely continuous spectrum of H = — d/dx + V(x) with F almost periodic and its discrete analog (hu)(n) = u(n +1) + u(n — 1) + V(ri)u(ri). Especial attention is paid to the set, A, of energies where the Lyaponov exponent vanishes. This set is known to be the essential support of the a.c. part of the spectral measure. We prove for a.e. Fin the hull and a.e. E in A, H and h have continuum eigenfunctions, u9 with \u\ almost periodic. In the discrete case, we prove that |^4|^4… CONTINUE READING

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