On a class of singular Sturm–Liouville problems
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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 $q=0.$References
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Bibliographic Information
- A. A. Vladimirov
- Affiliation: Institution of Russian Academy of Sciences, Dorodnicyn Computing Centre
- Email: vladimirov@shkal.math.msu.su
- Published electronically: April 1, 2020
- Additional Notes: The work has been supported by RSF (Russian Science Foundation) grant 17-11-01215.
- © Copyright 2020 American Mathematical Society
- Journal: Trans. Moscow Math. Soc. 2019, 211-219
- MSC (2010): Primary 34B24, 34B27
- DOI: https://doi.org/10.1090/mosc/295
- MathSciNet review: 4082869