Codimension of polynomial subspace in $L_2(\mathbb {R},d\mu )$ for discrete indeterminate measure $\mu$

Abstract:

A calculation formula is established for the codimension of the polynomial subspace in $L_2 ({\mathbb {R}}, d \mu )$ with discrete indeterminate measure $\mu$. We clarify how much the masspoint of the $n$-canonical solution of an indeterminate Hamburger moment problem differs from the masspoint of the corresponding $N$-extremal solution at a given point of the real axis.