Spectral distribution of a differential operator

On Spectral Asymptotics of the Neumann Problem for the Sturm–Liouville Equation with Self-Similar Weight of Generalized Cantor Type

“…An exact power exponent D of the counting function N (λ) in the case of a self-similar measure ρ was established in [7] (see also earlier papers [8] and [9] for partial results concerning the classical Cantor ladder).…”

Calculus on linear Cantor sets

“…Feller's diffusion operator, which is formally given by d dµ d dx (see [9] for details), is most easily defined using an inverse, i.e., integration with respect to µ followed by integration with respect to Lebesgue measure on [0, 1]. Identifying …”

“…Here, motivated by [2, Example IV 3.ε], we shall present a very simple first order calculus on Cantor subsets of the real line, whose associated Laplacian is the generalized differential operator studied in [9] slightly generalizing the diffusion operator of [3] (see also [4][5][6]). …”

Some Asymptotic Estimates of Transition Probability Densities for Generalized Diffusion Processes with Self-similar Speed Measures

“…For 0<a, $<*-, Q<a<b<l, consider the following eigenvalue problems where C 15 C 2 are positive constants (see [3], [4], [12]). Similarly, taking / 1 (jc)= rx+b l9 '" 3 Example, (de Rham function [13] or Bernoulli trial for unfair coin).…”