On spectral asymptotics of the Sturm–Liouville problem with self-conformal singular weight with strong bounded distortion property

Spectral asymptotics of the Neumann problem for the Sturm–Liouville equation with a singular self-conformal 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 the result obtained by T. Fujita (Taniguchi Symp. PMMP Katata, 1985) in the case of self-similar (self-affine) measure.