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Stability of Spectral Types for Sturm-Liouville Operators

del Rio, R. and Simon, B. and Stolz, G. (1994) Stability of Spectral Types for Sturm-Liouville Operators. Mathematical Research Letters, 1 (4). pp. 437-450. ISSN 1073-2780. https://resolver.caltech.edu/CaltechAUTHORS:20180719-140605491

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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.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.4310/MRL.1994.v1.n4.a4DOIArticle
ORCID:
AuthorORCID
Simon, B.0000-0003-2561-8539
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.
Funders:
Funding AgencyGrant Number
Dirección General de Asuntos del Personal Académico (DGAPA)UNSPECIFIED
Consejo Nacional de Ciencia y Tecnología (CONACYT)UNSPECIFIED
NSFDMS-9101715
Issue or Number:4
Record Number:CaltechAUTHORS:20180719-140605491
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20180719-140605491
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:88009
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:19 Jul 2018 21:17
Last Modified:03 Oct 2019 20:02

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