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

Сибирский математический журнал

article

U. R. Freiberg¹  N. V. Rastegaev² 

[1]Institut für Stochastik und Anwendungen

[2]Chebyshev Laboratory, St. Petersburg State University

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

DOI  :  10.1134/S0037446620050146

学科分类：数学（综合）

来源: Izdatel stvo Instituta Matematiki Rossiiskoi Akademii Nauk

【 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.

【 授权许可】

CC BY