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The non‐real spectrum of a singular indefinite Sturm–Liouville operator with regular left endpoint
Author(s) -
Behrndt Jussi,
Schmitz Philipp,
Trunk Carsten
Publication year - 2019
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201900133
Subject(s) - sturm–liouville theory , mathematics , spectrum (functional analysis) , interval (graph theory) , operator (biology) , mathematical analysis , differential operator , norm (philosophy) , pure mathematics , boundary value problem , combinatorics , physics , chemistry , quantum mechanics , repressor , political science , transcription factor , law , gene , biochemistry
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 .