Spectral asymptotics of the Neumann problem for the Sturm–Liouville equation with singular selfconformal weight measure is considered under the assumption of a stronger version of the bounded distortion property for the conformal iterated function system corresponding to the weight measure. The power exponent of the main term of the eigenvalue counting function asymptotics is obtained. This generalizes a result obtained by T. Fujita (1985) in the case of self-similar (selfaffine) measure.
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Published in Zapiski Nauchnykh Seminarov POMI, Vol. 477, 2018, pp. 129–135.
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Freiberg, U.R., Rastegaev, N.V. On Spectral Asymptotics of the Sturm–Liouville Problem with Self-Conformal Singular Weight with Strong Bounded Distortion Property. J Math Sci (2020) doi:10.1007/s10958-020-04671-x