George R. Exner, Professor of Mathematics
We indicate how our subject emerges from the confluence of several streams of analysis, including the classical moment problems, the theory of positive matrices and subnormal operator theory. Some new properties H(n (n, = 1,2, ..) and a Hamburger-type weighted shift are considered via a Hamburger moment sequence. We discuss examples to show the various H(n) are distinct; study flatness, backward n-step extensions and perturbations of weighted shifts; and, given three initial weights alpha(0), alpha(1), alpha(2) with alpha(0) <= alpha(2) < alpha(1), we produce a completion: a weighted shift of Hamburger type but not subnormal, extending a (subnormal) completion by Stampfli in the case alpha(0) < alpha(1) < alpha(2) (C) 2015 Elsevier Inc. All rights reserved.
Exner, George R.; Jinh, Joo Young; Jung, Ii Bong; and Lee, Mi Ryeong. “Weighted Shifts Induced by Hamburger Moment Sequences.” Journal of Mathematical Analysis and Applications 427, no. 2 (2015) : 581-599.