Spectral properties of singular Sturm—Liouville operators with indefinite weight sgn x
نویسندگان
چکیده
منابع مشابه
Spectral properties of singular Sturm-Liouville operators with indefinite weight sgnx
We consider a singular Sturm-Liouville expression with the indefinite weight sgnx. To this expression there is naturally a self-adjoint operator in some Krein space associated. 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 = (sgnx)(−d2/dx2 + q) with non-real sp...
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The indefinite Sturm-Liouville operator A = (sgnx)(−d2/dx2 + q(x)) is studied. It is proved that similarity of A to a selfadjoint operator is equivalent to integral estimates of Cauchy integrals. Also similarity conditions in terms of Weyl functions are given. For operators with a finite-zone potential, the components Aess and Adisc of A corresponding to essential and discrete spectrums, respec...
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ژورنال
عنوان ژورنال: Proceedings of the Royal Society of Edinburgh: Section A Mathematics
سال: 2009
ISSN: 0308-2105,1473-7124
DOI: 10.1017/s0308210507000686