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Spectral measure of commutative Jacobi field equipped with multiplication structure

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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 


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},
       URL = {http://mfat.imath.kiev.ua/article/?id=382},
}


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