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The multi-dimensional truncated moment problem: maximal masses

Konrad Schmüdgen
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Abstract

Given a subset $\mathcal K$ of $\mathbb R^d$ and a linear functional $L$ on the polynomials $\mathbb R^d_{2n}[\underline{x}]$ in $d$ variables and of degree at most $2n$ the truncated $\mathcal K$-moment problem asks when there is a positive Borel measure $\mu$ supported by $\mathcal K$ such that $L(p)=\int p\, d\mu$ for $p\in \mathbb R^d_{2n}[\underline{x}]$. For compact sets $\mathcal K$ we investigate the maximal mass of all representing measures at a given point of $\mathcal K$. Various characterizations of this quantity and related properties are developed and a close link to zeros of positive polynomials is established.

Key words: Moment problem, maximal mass, positive polynomial.


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Article Information

TitleThe multi-dimensional truncated moment problem: maximal masses
SourceMethods Funct. Anal. Topology, Vol. 21 (2015), no. 3, 266-281
MathSciNet   MR3521697
zbMATH 06630273
Milestones  Received 11/02/2015; Revised 28/02/2015
CopyrightThe Author(s) 2015 (CC BY-SA)

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Konrad Schmudgen
Universitat Leipzig, Mathematisches Institut, Augustusplatz 10/11, D-04109 Leipzig, Germany


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Konrad Schmüdgen, The multi-dimensional truncated moment problem: maximal masses, Methods Funct. Anal. Topology 21 (2015), no. 3, 266-281.


BibTex

@article {MFAT783,
    AUTHOR = {Schmüdgen, Konrad},
     TITLE = {The multi-dimensional truncated moment problem: maximal masses},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {21},
      YEAR = {2015},
    NUMBER = {3},
     PAGES = {266-281},
      ISSN = {1029-3531},
  MRNUMBER = {MR3521697},
 ZBLNUMBER = {06630273},
       URL = {http://mfat.imath.kiev.ua/article/?id=783},
}


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