Accumulation of complex eigenvalues of an indefinite Sturm--Liouville operator with a shifted Coulomb potential

Levitin, M. ORCID: https://orcid.org/0000-0003-0020-3265 and Seri, M. (2016) Accumulation of complex eigenvalues of an indefinite Sturm--Liouville operator with a shifted Coulomb potential. Operators and Matrices, 10 (1). pp. 223-245. ISSN 1848-9974 doi: 10.7153/oam-10-14

Abstract/Summary

For a particular family of long-range potentials V, we prove that the eigenvalues of the indefinite Sturm–Liouville operator A = sign(x)(−Δ+V(x)) accumulate to zero asymptotically along specific curves in the complex plane. Additionally, we relate the asymptotics of complex eigenvalues to the two-term asymptotics of the eigenvalues of associated self-adjoint operators.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/47043
Identification Number/DOI	10.7153/oam-10-14
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Uncontrolled Keywords	linear operator pencils; non-self-adjoint operators; Sturm--Liouville problem; Coulomb potential; complex eigenvalues; Kummer functions
Publisher	Publishing House Element d.o.o.
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