Critical and Subcritical Jacobi Operators Defined as Friedrichs Extensions

Motivated by a treatment of the Toda lattice and Kac-van Moerbeke equations we study critical and subcritical 2nd-order finite difference (Jacobi) operators T on . In the course of our analysis we also derive an explicit characterization of the Friedrichs extension TF of T in terms of principal solutions u± of Tu = 0 near ± ∞.