The essential spectrum of a singular Sturm–Liouville operator

Hernán Castro

Mathematische Nachrichten, 2018, vol. 291, issue 4, 593-609

Abstract: In this paper we study the essential spectrum of the operator LAu(x)=−(A(x)u′(x))′+u(x)where A(x) is a positive absolutely continuous function on (0, 1) that resembles x2α for some α≥1. We prove that the essential spectrum of LA coincides with the essential spectrum of the operator Lαu(x):=−(x2αu′(x))′+u(x).

Date: 2018
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https://doi.org/10.1002/mana.201600176

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