Point spectrum and mixed spectral types for rank one perturbations期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Point spectrum and mixed spectral types for rank one perturbations

Authors:	Rafael del Rio Barry Simon

Affiliation:	IIMAS-UNAM, Apdo. Postal 20-726, Admon. No.~20, Deleg Alvaro Obregon, 01000 Mexico, Mexico Barry Simon ; IIMAS-UNAM, Apdo. Postal 20-726, Admon. No.~20, Deleg Alvaro Obregon, 01000 Mexico, Mexico - Division of Physics, Mathematics, and Astronomy, California Institute of Technology, Pasadena, California 91125

Abstract:	We consider examples $A_{lambda }= A+lambda (varphi , ,cdot ,)varphi$ of rank one perturbations with a cyclic vector for . We prove that for any bounded measurable set , an interval, there exist so that ${Ein I mid text{some $A_{lambda }$ has $E$ as an}$ eigenvalue agrees with up to sets of Lebesgue measure zero. We also show that there exist examples where $A_{lambda }$ has a.c. spectrum for all , and for sets of 's of positive Lebesgue measure, $A_{lambda }$ also has point spectrum in , and for a set of 's of positive Lebesgue measure, $A_{lambda }$ also has singular continuous spectrum in .

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