Open Access

# 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.

### Article Information

 Title Spectral measure of commutative Jacobi field equipped with multiplication structure Source Methods Funct. Anal. Topology, Vol. 13 (2007), no. 1, 28-42 MathSciNet MR2308577 Copyright The 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},
}