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

[摘要] 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.

[学科分类] 数学（综合）

[关键词] spectral asymptotics;Sturm–Liouville operator;self-similar measure;self-conformal measure;bounded distortion property