Moment Infinitely Divisible Weighted Shifts

Authors

Raúl E. Curto, University of Iowa
Chafiq Benhida, Université des Sciences et Technologies de Lille
George R. Exner, BucknellFollow

Publication Date

2019

Description

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.

Journal

Complex Analysis and Operator Theory

Volume

13

Issue

1

First Page

241

Last Page

255

Department

Mathematics

DOI

https://doi.org/10.1007/s11785-018-0771-z

Recommended Citation

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