The essential spectrum of a singular Sturm–Liouville operator | Zendy

Castro Hernán | Zendy

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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 ) .

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