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Sibirskii Matematicheskii Zhurnal, 2020, Volume 61, Number 5, Pages 1130–1143
DOI: https://doi.org/10.33048/smzh.2020.61.514 (Mi smj6043) 		 
This article is cited in 1 scientific paper (total in 1 paper)

On spectral asymptotics of the sturm–liouville problem with self-conformal singular weight

U. R. Freiberga, N. V. Rastegaevb

a Institut für Stochastik und Anwendungen, Universität Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart, Germany
b Chebyshev Laboratory, St. Petersburg State University, Department of Mathematics and Mechanics
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DOI: https://doi.org/10.33048/smzh.2020.61.514
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.
Keywords: spectral asymptotics, Sturm–Liouville operator, self-similar measure, self-conformal measure, bounded distortion property.
Funding agency Grant number
Russian Science Foundation 19-71-30002
The authors were supported by the Russian Science Foundation (Grant 19–71–30002).
Received: 27.03.2020
Revised: 15.06.2020
Accepted: 17.06.2020
English version:
Siberian Mathematical Journal, 2020, Volume 61, Issue 5, Pages 901–912
DOI: https://doi.org/10.1134/S0037446620050146
Bibliographic databases:
Document Type: Article
UDC: 517.984.5
MSC: 35R30
Language: Russian
Citation: U. R. Freiberg, N. V. Rastegaev, “On spectral asymptotics of the sturm–liouville problem with self-conformal singular weight”, Sibirsk. Mat. Zh., 61:5 (2020), 1130–1143; Siberian Math. J., 61:5 (2020), 901–912
Citation in format AMSBIB
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