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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

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

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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