Abstract
For a particular family of long-range potentials V, we prove that the eigenvalues of the indefinite Sturm-Liouville operator A = sign(x)(-Delta+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.
| Original language | English |
|---|---|
| Pages (from-to) | 223-245 |
| Number of pages | 23 |
| Journal | Operators and matrices |
| Volume | 10 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - Mar-2016 |
Keywords
- Linear operator pencils
- non-self-adjoint operators
- Sturm-Liouville problem
- Coulomb potential
- complex eigenvalues
- Kummer functions
- DIFFERENTIAL-OPERATORS
- SIMILARITY PROBLEM
- SGN X