The non‐real spectrum of a singular indefinite Sturm–Liouville operator with regular left endpoint. Issue 1 (18th November 2019)

• Record Type: Journal Article
• Authors: Behrndt, Jussi; Schmitz, Philipp; Trunk, Carsten
• Other Names: Eberhardsteiner J. guestEditor.; Schöberl M. guestEditor.
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 19:Issue 1(2019)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2019-11-18
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.201900133
• Languages: English
• ISSNs: 1617-7061

Abstract

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 .