Moment Infinitely Divisible Weighted Shifts
Complex Analysis and Operator Theory
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.
Curto, Raúl E.; Benhida, Chafiq; and Exner, George R.. "Moment Infinitely Divisible Weighted Shifts." Complex Analysis and Operator Theory (2019) : 241-255.