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M. Langer, H. Woracek:
"Stability of N-extremal measures";
in: "ASC Report 05/2013", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2013, ISBN: 978-3-902627-06-3, 1 - 8.

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 ad- dition, µ generates an indeterminate Hamburger
moment problem, then it is discrete. It is known that the class of N-extremal measure 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.

Hamburger moment problem, N-extremal measure, perturbation of support

http://www.asc.tuwien.ac.at/preprint/2013/asc05x2013.pdf