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The essential spectrum of a singular Sturm–Liouville operator
Author(s) -
Castro Hernán
Publication year - 2018
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201600176
Subject(s) - mathematics , essential spectrum , spectrum (functional analysis) , operator (biology) , sturm–liouville theory , absolute continuity , function (biology) , pure mathematics , mathematical analysis , quantum mechanics , physics , boundary value problem , biochemistry , chemistry , repressor , evolutionary biology , biology , transcription factor , gene
In this paper we study the essential spectrum of the operatorL A u ( x ) = − ( A ( x ) u ′ ( x ) ) ′ + u ( x )where A ( x ) is a positive absolutely continuous function on (0, 1) that resembles x 2 αfor some α ≥ 1 . We prove that the essential spectrum of L A coincides with the essential spectrum of the operatorL α u ( x ) : = − ( x 2 αu ′ ( x ) ) ′ + u ( x ) .