Distribution of spectrum in limit point case without full spectral asymptotics

Develop results that give quantitative control of the eigenvalue-counting function or spectral distribution for Jacobi operators or canonical systems in limit point case without assuming a full spectral asymptotic expansion, i.e., provide density or type bounds analogous to the limit circle case.

Background

While the limit point case has a substantial literature on detailed spectral asymptotics, there appear to be no results that provide large-scale spectral distribution bounds (e.g., growth of the counting function) without deriving full asymptotic expansions.

Filling this gap would mirror the density-oriented theory developed for the limit circle case and extend it to operators with limit point behaviour.