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Functional Analysis and Its Applications

, Volume 52, Issue 1, pp 70–73 | Cite as

On Spectral Asymptotics of the Neumann Problem for the Sturm–Liouville Equation with Arithmetically Self-Similar Weight of a Generalized Cantor Type

  • N. V. Rastegaev
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Abstract

Spectral asymptotics of the Sturm–Liouville problem with an arithmetically self-similar singular weight is considered. Previous results by A. A. Vladimirov and I. A. Sheipak, and also by the author, rely on the spectral periodicity property, which imposes significant restrictions on the self-similarity parameters of the weight. This work introduces a new method for estimating the eigenvalue counting function. This makes it possible to consider a much wider class of self-similar measures.

Key words

spectral asymptotics semi-similar measure 

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References

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Chebyshev LaboratorySaint Petersburg State UniversitySt. PetersburgRussia

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