The investigation of a generalized moment problem associated with correlation measures

Abstract

The classical power moment problem can be viewed as a theory of spectral representations of a positive functional on some classical commutative algebra with involution. We generalize this approach to the case where the algebra is a special commutative algebra of functions on the space of multiple finite configurations.

If the above-mentioned functional is generated by a measure on the space of usual finite configurations then this measure is a correlation measure for a probability spectral measure on the space of infinite configurations. The latter measure is practically arbitrary, so that we have a connection between this complicated measure and its correlation measure defined on more simple objects that are finite configurations. The paper gives an answer to the following question: when this latter measure is a correlation measure for a complicated measure on infinite configurations? (Such measures are essential objects of statistical mechanics).

Key words: Convolution, positive functional, finite and infinite configurations, generalized joint eigenvector, correlation measure.

Full Text

Article Information

Title	The investigation of a generalized moment problem associated with correlation measures
Source	Methods Funct. Anal. Topology, Vol. 13 (2007), no. 2, 124-151
MathSciNet	MR2336717
Copyright	The Author(s) 2007 (CC BY-SA)

Authors Information

Yu. M. Berezansky
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs'ka, Kyiv, 01601, Ukraine

D. A. Mierzejewski
Zhytomyr State University, Zhytomyr, Ukraine 

Citation Example

Yu. M. Berezansky and D. A. Mierzejewski, The investigation of a generalized moment problem associated with correlation measures, Methods Funct. Anal. Topology 13 (2007), no. 2, 124-151.

BibTex

@article {MFAT402,
    AUTHOR = {Berezansky, Yu. M. and Mierzejewski, D. A.},
     TITLE = {The investigation of a generalized moment problem associated with correlation measures},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {13},
      YEAR = {2007},
    NUMBER = {2},
     PAGES = {124-151},
      ISSN = {1029-3531},
  MRNUMBER = {MR2336717},
       URL = {http://mfat.imath.kiev.ua/article/?id=402},
}