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.

Full Text

Article Information

Title	The two-dimensional moment problem in a strip
Source	Methods Funct. Anal. Topology, Vol. 19 (2013), no. 1, 40-54
MathSciNet	MR3088317
zbMATH	1289.47032
Milestones	Received 09/04/2012; Revised 27/10/2012
Copyright	The 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 

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},
}