Stationary Fourier hyperprocesses
type: Item
instance of: scholarly article
title: Stationary Fourier hyperprocesses
zbMATH Open document ID: 0604.60039
author: Yoshifumi Ito
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 1986-01-01T00:00:00Z
review text: This is an application of the theory of vector valued Fourier hyperfunctions. In this paper, the author defined a concept of stationary Fourier hyperprocesses and studied their properties. A random Fourier hyperprocess is defined to be a vector valued Fourier hyperfunction on \({\mathbb{D}}=[-\infty,\infty]\) whose values are random variables with mean 0 and finite variance. Then he defined a concept of stationary (random) Fourier hyperprocesses. At first, he showed the existence of the covariance Fourier hyperfunction of a stationary Fourier hyperprocess. Next, he showed that this covariance Fourier hyperfunction \(\rho\) is the Fourier transform of a nonnegative measure \(\mu\) with infraexponential increase. This measure \(\mu\) is called the spectral measure of \(\rho\). At last he proved that any stationary Fourier hyperprocess is the Fourier transform of a random hypomeasure with respect to the spectral measure of its covariance Fourier hyperfunction. Here we note that Theorem 3.3 and Theorem 3.5 should be omitted because its assertions are incorrect.
Mathematics Subject Classification ID: 60G20
Mathematics Subject Classification ID: 60G10
Mathematics Subject Classification ID: 46F15
zbMATH DE Number: 3976005
zbMATH Keywords: vector valued Fourier hyperfunctions
zbMATH Keywords: stationary Fourier hyperprocesses
zbMATH Keywords: spectral measure
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1195178370
OpenAlex ID: W2050484463
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DOI: 10.2977/PRIMS/1195178370
description: scientific article; zbMATH DE number 3976005