Spectral Properties of Differential Operators with Oscillating Coefficients

Valeev, N.; Sultanaev, Ya.; Nazirova, É.

doi:10.1090/mosc/299

Spectral Properties of Differential Operators with Oscillating Coefficients
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by N. F. Valeev, Ya. T. Sultanaev and É. A. Nazirova
Translated by: V. E. Nazaikinskii

Trans. Moscow Math. Soc. 2019, 153-167

DOI: https://doi.org/10.1090/mosc/299

Published electronically: April 1, 2020

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Abstract:

We study the properties of singular Sturm–Liouville operators in Hilbert spaces. Although the literature on the topic is immense, there are a number of questions that have yet to be solved, for example, those pertaining to the behavior of solutions of the Sturm–Liouville equation with an irregular potential at infinity. This problem is topical not only for being of interest in itself but also because it naturally arises when dealing with questions related to the spectral properties of the Sturm–Liouville operator.

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