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The two-dimensional moment problem in a strip


Abstract

In this paper we study the two-dimensional moment problem in a strip $\Pi(R) = \{ (x_1,x_2)\in \mathbb{R}^2:\ |x_2| \leq R \}$, $R>0$. We obtained an analytic parametrization of all solutions of this moment problem. Usually the problem is reduced to an extension problem for a pair of commuting symmetric operators but we have no possibility to construct such extensions in larger spaces in a direct way. It turns out that we can find solutions without knowing the corresponding extensions in larger spaces. We used the fundamental results of Shtraus on generalized resolvents and some results from the measure theory.

Key words: Moment problem, measure, generalized resolvent.


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Article Information

TitleThe two-dimensional moment problem in a strip
SourceMethods Funct. Anal. Topology, Vol. 19 (2013), no. 1, 40-54
MathSciNet MR3088317
zbMATH 1289.47032
MilestonesReceived 09/04/2012; Revised 27/10/2012
CopyrightThe Author(s) 2013 (CC BY-SA)

Authors Information

S. M. Zagorodnyuk
School of Mathematics and Mechanics, Karazin Kharkiv National University, 4 Svobody sq., Kharkiv, 61077, Ukraine 


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Citation Example

S. M. Zagorodnyuk, The two-dimensional moment problem in a strip, Methods Funct. Anal. Topology 19 (2013), no. 1, 40-54.


BibTex

@article {MFAT648,
    AUTHOR = {Zagorodnyuk, S. M.},
     TITLE = {The two-dimensional moment problem in a strip},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {19},
      YEAR = {2013},
    NUMBER = {1},
     PAGES = {40-54},
      ISSN = {1029-3531},
  MRNUMBER = {MR3088317},
 ZBLNUMBER = {1289.47032},
       URL = {http://mfat.imath.kiev.ua/article/?id=648},
}


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