The non‐real spectrum of a singular indefinite Sturm–Liouville operator with regular left endpoint

Abstract

We provide bounds on the non-real spectra of indefinite Sturm-Liouville differential operators of the form (Af )(x) = sgn(x)(−f (x) + q(x)f (x)) on the interval [a, ∞), −∞ < a < 0, with real potential q ∈ L 1 (a, ∞). The bounds depend only on the L 1 -norm of the negative part of q and the boundary condition at the regular endpoint a.