On a class of singular Sturm–Liouville problems

Vladimirov, A.

doi:10.1090/mosc/295

On a class of singular Sturm–Liouville problems
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by A. A. Vladimirov
Translated by: A. S. Kirpichnikova

Trans. Moscow Math. Soc. 2019, 211-219

DOI: https://doi.org/10.1090/mosc/295

Published electronically: April 1, 2020

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Abstract:

A formally self-adjoint boundary value problem is under consideration. It corresponds to the formal differential equation $-(y’/r)’+q{}y=p{}f$, where $r$ and $p$ are generalized densities of two Borel measures which do not have common atoms and $q$ is a generalized function from some class related to the density $r.$ A self-adjoint operator generated by this boundary value problem is defined. The main term of the spectral asymptotics is established in the case when $r$ and $p$ are self-similar and $q=0.$

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