Boundary conditions of Sturm-Liouville operators with mixed spectra
We study bounds on averages of spectral functions corresponding to Sturm-Liouville operators on the half line for different boundary conditions. As a consequence constraints are obtained which imply existence of singular spectrum embedded in a.c. spectrum for sets of boundary conditions with positiv...
| Authors: | , |
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| Format: | article |
| Status: | Published version |
| Publication Date: | 2003 |
| Country: | México |
| Institution: | Universidad Nacional Autónoma de México |
| Repository: | Sistema de Información de la Facultad de Ciencias, UNAM |
| OAI Identifier: | oai:repositorio.fciencias.unam.mx:11154/1663 |
| Online Access: | http://hdl.handle.net/11154/1663 |
| Access Level: | Open access |
| Keyword: | Mathematics, Applied Mathematics Sturm-Liouville operator mixed spectra spectral measure |
| Summary: | We study bounds on averages of spectral functions corresponding to Sturm-Liouville operators on the half line for different boundary conditions. As a consequence constraints are obtained which imply existence of singular spectrum embedded in a.c. spectrum for sets of boundary conditions with positive measure and potentials vanishing in an interval [0, N]. These constraints are related to estimates on the measure of sets where the spectral density is positive. (C) 2003 Elsevier Inc. All rights reserved. |
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