A note about the deterministic property of characteristic functions-Reference-Cited by-同舟云学术

A note about the deterministic property of characteristic functions

Published:2018-12-20 Issue:1 Volume:24 Page:150-158
ISSN:1392-5113
Container-title:Nonlinear Analysis: Modelling and Control
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Author:

Norvidas Saulius¹

Affiliation:

1. Institute of Data Science and Digital Technologies, Vilnius University

Abstract

We study an extension property for characteristic functions f : Rn → C of probability measures. More precisely, let f be the characteristic function of a probability density φ on Rn, and let Uσ = {x ∈ Rn: mink|xk| > σ}, σ > 0, be a neighborhood of infinity. We say that f has the σ-deterministic property if for any other characteristic function g such that f = g on Uσ, it follows that f ≡ g. A sufficient condition on f to has the σ-deterministic property is given. We also discuss the question about how precise our sufficient condition is? These results show that the σ-deterministic property of f depends on an arithmetic structure of the support of φ.

Publisher

Vilnius University Press

Subject

Applied Mathematics,Analysis

Reference9 articles.

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