In:
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, Cambridge University Press (CUP), Vol. 139, No. 3 ( 2009-10), p. 483-503
Abstract:
We consider a singular Sturm—Liouville expression with the indefinite weight sgn x . There is a self-adjoint operator in some Krein space associated naturally with this expression. We characterize the local definitizability of this operator in a neighbourhood of ∞. Moreover, in this situation, the point ∞ is a regular critical point. We construct an operator A = (sgn x )(−d 2 /d x 2 + q ) with non-real spectrum accumulating to a real point. The results obtained are applied to several classes of Sturm—Liouville operators.
Type of Medium:
Online Resource
ISSN:
0308-2105
,
1473-7124
DOI:
10.1017/S0308210507000686
Language:
English
Publisher:
Cambridge University Press (CUP)
Publication Date:
2009
detail.hit.zdb_id:
209230-X
detail.hit.zdb_id:
2036780-6
SSG:
11
Bookmarklink