Accumulation of complex eigenvalues of an indefinite Sturm-Liouville operator with a shifted Coulomb potential
Accumulation of complex eigenvalues of an indefinite Sturm-Liouville operator with a shifted Coulomb potential
For a particular family of long-range potentials $V$, we prove that the eigenvalues of the indefinite Sturm--Liouville operator $A = \mathrm{sign}(x)(-Δ+ V(x))$ 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 …