Title

Weighted Shifts Induced by Hamburger Moment Sequences

Publication Date

2015

Journal

Journal of Mathematical Analysis and Applications

Volume

427

Issue

2

First Page

581

Last Page

599

Abstract

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.

DOI

10.1016/j.jmaa.2015.02.033

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