Dispersive decay estimates for periodic Jacobi operators on the half-line

We establish dispersive time-decay estimates for periodic Jacobi operators on the discrete half-line, N. Specifically, we prove t^−1/2 decay in the weighted ℓ₋₁^∞ norm for all such operators. For the global ℓ¹→ℓ^∞ decay estimate, we show that t^−1/3 decay holds under a nondegeneracy condition on the discriminant. Alternatively, for any even period q≥2, if the continuous spectrum consists of exactly q disjoint intervals (bands), we obtain a t^−1/(q+1) decay rate without any further assumptions.