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Published November 1996 | public
Journal Article

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

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.

Additional Information

© Copyright 1996 Barry Simon. Communicated by: Palle E. T. Jorgensen. Received by the editors April 3, 1995 and, in revised form, April 24, 1995. This material is based upon work supported by the National Science Foundation under Grant No. DMS-9401491. The Government has certain rights in this material.

Additional details

Created:
August 19, 2023
Modified:
October 18, 2023