Analogue of κ_H-based algorithmic bounds for the limit point case

Develop an analogue, for canonical systems in the limit point case, of the algorithmic bounds that relate the partition-count κ_H(r) to the growth of the monodromy matrix norm in the limit circle case. Construct a corresponding quantity and inequalities (e.g., in terms of the Weyl coefficient) that yield comparable lower and upper bounds for spectral-growth measures when the monodromy matrix is not available.

Background

In the limit circle case, an explicit algorithm partitions the interval using det ΩH to define κ_H(r), and yields lower and upper bounds for \log(max{|z|=r} ||W_H(z)||). This provides a practical way to estimate growth from the Hamiltonian’s local rotation behaviour.

No such algorithm is known for the limit point case, where the fundamental solution does not extend to the endpoint and the Weyl coefficient is the right analytic object. An analogue would extend these effective growth estimates to a much broader class of systems.