CaltechAUTHORS
Published 1994 | public
Journal Article Metadata-only

Stability of Spectral Types for Sturm-Liouville Operators

del Rio, R.
Simon, B. ORCID icon
Stolz, G.
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Abstract

For Sturm-Liouville operators on the half line, we show that the property of having singular, singular continuous, or pure point spectrum for a set of boundary conditions of positive measure depends only on the behavior of the potential at infinity. We also prove that existence of recurrent spectrum implies that of singular spectrum and that "almost sure" existence of L_2-solutions implies pure point spectrum for almost every boundary condition. The same results hold for Jacobi matrices on the discrete half line.

Additional Information

© 1994 International Press of Boston. Received March 7, 1994. The work of R. del Rio is partially supported by DGAPA-UNAM and CONACYT. The work of R. del Rio and B. Simon is partially supported by the National Science Foundation under Grant No. DMS-9101715. The Government has certain rights in this material. R. del Rio would like to thank J. Weidmann for having initiated him in the study of stability of spectral types. R.del Rio and G.Stolz would also like to thank C. Peck and M. Aschbacher for the hospitality at Caltech.

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August 20, 2023
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October 18, 2023