Asymptotics of the spectrum of a differential operator with the weight generated by the Minkowski function
Igor Anatolievich Sheipak · Mathematical Notes · 2015
This paper is devoted to the study of the asymptotics of the spectrum of the boundary-value problem $ - y'' - \lambda \rho y = 0,y(0) = y(1) = 0,$ where ρ is the generalized derivative of the Minkowski function, i.e., ρ =?′(x) (here ?(x) is the “question-mark function” first defined by Minkowski, who introduced this notation). For the eigenvalues of the problem, asymptotic two-sided estimates of power type are obtained. The order of the power is determined by the Hausdorff dimension of the support of the Minkowski measure d?.