Moment Infinitely Divisible Weighted Shifts
We say that a weighted shift Wα with (positive) weight sequence α : α0, α1,... is moment infinitely divisible (MID) if, for every t > 0, the shift with weight sequence αt : αt 0, αt 1,... is subnormal. Assume that Wα is a contraction, i.e., 0 < αi ≤ 1 for all i ≥ 0. We show that such a shift Wα is MID if and only if the sequence α is log completely alternating. This enables the recapture or improvement of some previous results proved rather differently. We derive in particular new conditions sufficient for subnormality of a weighted shift, and each example contains implicitly an example or family of infinitely divisible Hankel matrices, many of which appear to be new.
Complex Analysis and Operator Theory
Curto, Raúl E.; Benhida, Chafiq; and Exner, George R.. "Moment Infinitely Divisible Weighted Shifts." Complex Analysis and Operator Theory (2019) : 241-255.