IUMJ

Title: Naimark extensions for indeterminacy in the moment problem. An example

Authors: Dariusz Cichon, Jan Stochel and Franciszek Hugon Szafraniec

Issue: Volume 59 (2010), Issue 6, 1947-1970

Abstract:

Using the possibility of extending a symmetric operator to a selfadjoint one, which goes beyond the Hilbert space, we construct an example (in fact a class of them) of an indeterminate Hamburger moment sequence admitting a family of representing measures such that: the support of each of them is in \emph{arithmetic} progression, the supports of all the measures together partition $\mathbb{R}$, none of them is N-extremal, and all of them are of infinite order. In fact, our goal is twofold: to present an example and to propose a method which may be useful for obtaining other results of this kind.