Asymptotics of eigenvalues of Sturm--Liouville problem with discrete self-similar weight

Abstract

The Sturm--Liouville problem $-y^{\prime \prime }-\lambda \rho y=0$, $y(0)=y(1)=0$, where $\rho$ is a generalized derivative of self-similar function $P\in L_2[0,1]$ with spectral degree D=0, is studied. Asymptotic formulas for eigenvalues are obtained.

8 pages, 3 tables

Cited by in corpus (1)

• Degenerate self-similar measures, spectral asymptotics and small deviations of Gaussian processes