Orthogonal Laurent polynomials and the strong Hamburger moment problem (Q791091)

By a strong Hamburger moment problem, we understand that if a doubly infinite sequence \(\{c_ n\}^{\infty}\!_{-\infty}\) of real numbers is given then we have to find necessary and sufficient conditions for the existence of a bounded, real-valued, non-decreasing function \(\psi\) on (- \(\infty,\infty)\) with infinitely many points of increase, such that \[ c_ n=\int^{\infty}_{-\infty}(-t)^ nd\psi(t),\quad n=0,\pm 1,\pm 2,.... \] The authors investigate the solution of this problem. The solution given by the authors is in terms of positivity of certain Hankel determinants associated with the double sequence \(\{c_ n\}\). The main tool employed in the proof is the theory of orthogonal (and quasi- orthogonal) Laurent polynomials.