Stability of N-extremal measures

Matthias Langer, Harald Woracek

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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.
Original languageEnglish
Pages (from-to)69-75
Number of pages7
JournalMethods of Functional Analysis and Topology
Volume21
Issue number1
Publication statusPublished - Mar 2015

Keywords

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

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