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Tr. Mosk. Mat. Obs., 2019, Volume 80, Issue 2, Pages 247–257 (Mi mmo629)  

On a class of singular Sturm–Liouville problems

A. A. Vladimirov

Institution of Russian Academy of Sciences, Dorodnicyn Computing Centre

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.$

Key words and phrases: Sturm–Liouville problem, Sobolev space, generalized function, self-similar measure.

Funding Agency Grant Number
Russian Science Foundation 17-11-01215
The work has been supported by RSF (Russian Science Foundation) grant 17-11-01215.


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English version:
Transactions of the Moscow Mathematical Society, 2019, 80, 211–219

UDC: 517.984
MSC: 34B24, 34B27
Received: 31.05.2019

Citation: A. A. Vladimirov, “On a class of singular Sturm–Liouville problems”, Tr. Mosk. Mat. Obs., 80, no. 2, MCCME, M., 2019, 247–257; Trans. Moscow Math. Soc., 80 (2019), 211–219

Citation in format AMSBIB
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\by A.~A.~Vladimirov
\paper On a class of singular Sturm--Liouville problems
\serial Tr. Mosk. Mat. Obs.
\yr 2019
\vol 80
\issue 2
\pages 247--257
\publ MCCME
\publaddr M.
\mathnet{http://mi.mathnet.ru/mmo629}
\elib{https://elibrary.ru/item.asp?id=43272481}
\transl
\jour Trans. Moscow Math. Soc.
\yr 2019
\vol 80
\pages 211--219
\crossref{https://doi.org/10.1090/mosc/295}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85083802401}


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