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

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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

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To link to this item 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
Refereed:Yes
Divisions:Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:47043
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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