Stability of N-extremal measures

Matthias Langer, Harald Woracek

Research output: Contribution to journalArticle

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.
LanguageEnglish
Pages69-75
Number of pages7
JournalMethods of Functional Analysis and Topology
Volume21
Issue number1
Publication statusPublished - Mar 2015

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Indeterminate Moment Problems
Borel Measure
Moment
Perturbation
Polynomial
Class

Keywords

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

Cite this

Langer, Matthias ; Woracek, Harald. / Stability of N-extremal measures. In: Methods of Functional Analysis and Topology. 2015 ; Vol. 21, No. 1. pp. 69-75.
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Stability of N-extremal measures. / Langer, Matthias; Woracek, Harald.

In: Methods of Functional Analysis and Topology, Vol. 21, No. 1, 03.2015, p. 69-75.

Research output: Contribution to journalArticle

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