Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9495441 | Journal of Functional Analysis | 2005 | 45 Pages |
Abstract
Let S be the orthogonal sum of infinitely many pairwise unitarily equivalent symmetric operators with non-zero deficiency indices. Let J be an open subset of R. If there exists a self-adjoint extension S0 of S such that J is contained in the resolvent set of S0 and the associated Weyl function of the pair {S,S0} is monotone with respect to J, then for any self-adjoint operator R there exists a self-adjoint extension SË such that the spectral parts SËJ and RJ are unitarily equivalent. It is shown that for any extension SË of S the absolutely continuous spectrum of S0 is contained in that one of SË. Moreover, for a wide class of extensions the absolutely continuous parts of SË and S are even unitarily equivalent.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
S. Albeverio, J.F. Brasche, M.M. Malamud, H. Neidhardt,