This article is cited in 2 papers

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

U. R. Freiberg^a, N. V. Rastegaev<sup>b

a</sup> 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

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.

UDC: 517.984.5

MSC: 35R30

Received: 27.03.2020
Revised: 15.06.2020
Accepted: 17.06.2020

DOI: 10.33048/smzh.2020.61.514

 English version: Siberian Mathematical Journal, 2020, 61:5, 901–912

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