Naimark extensions for indeterminacy in the moment problem. An example Dariusz CichonJan StochelFranciszek Szafraniec 44A6047A5730E05Hamburger moment sequenceindeterminate moment sequenceN-extremal measureorder of a representing measureFourier transformPaley-Wiener spaceWhittaker-Shannon-Kotelnikov samplingselfadjoint extension 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. Indiana University Mathematics Journal 2010 text pdf 10.1512/iumj.2010.59.4380 10.1512/iumj.2010.59.4380 en Indiana Univ. Math. J. 59 (2010) 1947 - 1970 state-of-the-art mathematics http://iumj.org/access/