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Spectral measure of commutative Jacobi field equipped with multiplication structure


Abstract

The article investigates properties of the spectral measure of the Jacobi field constructed over an abstract Hilbert rigging $H_-\supset H\supset L\supset H_+.$ Here $L$ is a real commutative Banach algebra that is dense in $H.$ It is shown that with certain restrictions, the Fourier transform of the spectral measure can be found in a similar way as it was done for the case of the Poisson field with the zero Hilbert space $L^2(\Delta,d u).$ Here $\Delta$ is a Hausdorff compact space and $ u$ is a probability measure defined on the Borel $\sigma$-algebra of subsets of $\Delta.$ The article contains a formula for the Fourier transform of a spectral measure of the Jacobi field that is constructed over the above-mentioned abstract rigging.


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Article Information

TitleSpectral measure of commutative Jacobi field equipped with multiplication structure
SourceMethods Funct. Anal. Topology, Vol. 13 (2007), no. 1, 28-42
MathSciNet   MR2308577
CopyrightThe Author(s) 2007 (CC BY-SA)

Authors Information

Oleksii Mokhonko
Taras Shevchenko Kyiv National University, Kyiv, Ukraine 


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Citation Example

Oleksii Mokhonko, Spectral measure of commutative Jacobi field equipped with multiplication structure, Methods Funct. Anal. Topology 13 (2007), no. 1, 28-42.


BibTex

@article {MFAT382,
    AUTHOR = {Mokhonko, Oleksii},
     TITLE = {Spectral measure of commutative Jacobi field equipped with multiplication structure},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {13},
      YEAR = {2007},
    NUMBER = {1},
     PAGES = {28-42},
      ISSN = {1029-3531},
  MRNUMBER = {MR2308577},
       URL = {http://mfat.imath.kiev.ua/article/?id=382},
}


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