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Stability of essential spectra of singular Sturm‐Liouville differential operators under perturbations small at infinity
Author(s) -
Sun Huaqing,
Qi Jiangang
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4730
Subject(s) - mathematics , sturm–liouville theory , infinity , operator (biology) , differential operator , mathematical analysis , spectrum (functional analysis) , essential spectrum , stability (learning theory) , spectral line , pure mathematics , physics , chemistry , quantum mechanics , boundary value problem , biochemistry , repressor , transcription factor , gene , machine learning , computer science
This paper is concerned with the stability of essential spectra of singular Sturm‐Liouville differential operators with complex‐valued coefficients. It is proved that the essential spectrum of the corresponding minimal operator is preserved by perturbations small at infinity with respect to the unperturbed operator. Based on it, 1‐dimensional Schrödinger operators under local dilative perturbations are studied.