M. Langer and H. Woracek,
Stability of N-extremal measures,
Methods Funct. Anal. Topology 21 (2015), 69–75
Abstract:
A positive Borel measure μ on ℝ, which possesses all power moments,
is N-extremal if the space of all polynomials is dense in L2(μ).
If, in addition, μ generates an indeterminate Hamburger moment problem, then it is discrete.
It is known that the class of N-extremal measures that generate an indeterminate
moment problem is preserved when a finite number of mass points are moved
(not “removed”!).
We show that this class is preserved even under change of infinitely many mass points if the
perturbations are asymptotically small. Thereby “asymptotically small” is
understood relative to the distribution of
supp μ; for example, if
supp μ={nσ log n:
n∈ℕ}
with some σ > 2,
then shifts of mass points behaving asymptotically
like, e.g. nσ-2[log log n]–2 are permitted.