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...

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Bibliographic Details
Authors: del Rio, R, Tchebotareva, O
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
Description
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.