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On Spectral Asymptotics of the Sturm–Liouville Problem with Self-Conformal Singular Weight

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Abstract

Under study is the spectral asymptotics of the Sturm–Liouville problem with a singular self-conformal weight measure. We assume that the conformal iterated function system generating the weight measure satisfies a stronger version of the bounded distortion property. The power exponent of the main term of the eigenvalue counting function asymptotics is obtained under the assumption. This generalizes the result by Fujita in the case of self-similar (self-affine) measures.

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Acknowledgment

The authors thank A. I. Nazarov for the attention to this research and valuable remarks.

Funding

The authors were supported by the Russian Science Foundation (Grant 19–71–30002).

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Authors and Affiliations

  1. Universität Stuttgart, Institut für Stochastik und Anwendungen, Stuttgart, Germany

    U. R. Freiberg

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

    N. V. Rastegaev

Authors
  1. U. R. Freiberg
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  2. N. V. Rastegaev
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Correspondence to U. R. Freiberg.

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Freiberg, U.R., Rastegaev, N.V. On Spectral Asymptotics of the Sturm–Liouville Problem with Self-Conformal Singular Weight. Sib Math J 61, 901–912 (2020). https://doi.org/10.1134/S0037446620050146

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  • DOI: https://doi.org/10.1134/S0037446620050146

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