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Funktsional. Anal. i Prilozhen., 2018, Volume 52, Issue 1, Pages 85–88 (Mi faa3469)  

This article is cited in 1 scientific paper (total in 1 paper)

Brief communications

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

Chebyshev Laboratory, Saint Petersburg State University, St. Petersburg, Russia

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.

Keywords: spectral asymptotics, semi-similar measure.

Funding Agency Grant Number
Saint Petersburg State University 6.65.37.2017
Russian Foundation for Basic Research 16-01-00258а
This work is supported by the joint SPbU-DFG grant No. 6.65.37.2017 and by RFBR grant (project 16-01-00258a).


DOI: https://doi.org/10.4213/faa3469

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English version:
Functional Analysis and Its Applications, 2018, 52:1, 70–73

Bibliographic databases:

UDC: 517.927.25
Received: 23.04.2017

Citation: N. V. Rastegaev, “On Spectral Asymptotics of the Neumann Problem for the Sturm–Liouville Equation with Arithmetically Self-Similar Weight of a Generalized Cantor Type”, Funktsional. Anal. i Prilozhen., 52:1 (2018), 85–88; Funct. Anal. Appl., 52:1 (2018), 70–73

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. U. R. Freiberg, N. V. Rastegaev, “On spectral asymptotics of the Sturm–Liouville problem with self-conformal singular weight with strong bounded distortion property”, Kraevye zadachi matematicheskoi fiziki i smezhnye voprosy teorii funktsii. 47, K 85-letiyu Vsevoloda Alekseevicha SOLONNIKOVA, Zap. nauchn. sem. POMI, 477, POMI, SPb., 2018, 129–135  mathnet
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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