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

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.

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Correspondence to N. V. Rastegaev.

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Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 52, No. 1, pp. 85–88, 2018

Original Russian Text Copyright © by N. V. Rastegaev

This work is supported by the joint SPbU-DFG grant No. 6.65.37.2017 and by RFBR grant (project 16-01-00258a).

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Rastegaev, N.V. On Spectral Asymptotics of the Neumann Problem for the Sturm–Liouville Equation with Arithmetically Self-Similar Weight of a Generalized Cantor Type. Funct Anal Its Appl 52, 70–73 (2018). https://doi.org/10.1007/s10688-018-0211-x

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Key words

  • spectral asymptotics
  • semi-similar measure