Bounded eigenfunctions and absolutely continuous spectra for one-dimensional Schrödinger operators

Simon, Barry

doi:10.1090/S0002-9939-96-03599-X

Bounded eigenfunctions and absolutely continuous spectra for one-dimensional Schrödinger operators
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Proc. Amer. Math. Soc. 124 (1996), 3361-3369

Abstract:

We provide a short proof of that case of the Gilbert-Pearson theorem that is most often used: That all eigenfunctions bounded implies purely a.c. spectrum. Two appendices illuminate Weidmann’s result that potentials of bounded variation have strictly a.c. spectrum on a half-axis.

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