Curiosities of characteristic functions
type: Item
instance of: scholarly article
title: Curiosities of characteristic functions
zbMATH Open document ID: 0995.60017
DOI: 10.1016/S0723-0869(01)80020-7
author: Tilmann Gneiting
published in: Expositiones Mathematicae
publication date: 2002-05-14T00:00:00Z
review text: The author proves the following two theorems. Theorem 1. For each symmetric closed subset of the real line \(\mathbb{R}\) that contains the origin there exist characteristic functions \(\varphi(t)\) and \(\psi(t)\) such that \(\varphi(t)= \psi(t)\) on this set and \(\varphi(t)\neq \psi(t)\) otherwise. Theorem 2. Let \(\varphi\) be the characteristic function of an absolutely continuous distribution with a continuous, strictly positive density. Then there exists, for each \(a>0\), a characteristic function \(\psi(t)\) such that \(\varphi(t)= \psi(t)\) if \(t= 0\) or \(|t|> a\) and \(\varphi(t)\neq \psi(t)\) otherwise. An interesting open problem is formulated.
Mathematics Subject Classification ID: 60E10
zbMATH DE Number: 1740122
zbMATH Keywords: characteristic functions
MaRDI profile type: Publication
cites work: Q5512461
cites work: Simple tests for the validity of correlation function models on the circle
cites work: On the Zeros and the Argument of a Characteristic Function
cites work: Krein's strings, the symmetric moment problem, and extending a real positive definite function
cites work: Quelques problèmes non résolus de la théorie des fonctions caractéristiques
cites work: Q5598785
cites work: Characteristic functions taking constant values on intervals of the real line
cites work: Über die Nullstellenmenge von charakteristischen Funktionen
cites work: Selected Topics in Characteristic Functions
cites work: Error estimates for interpolation by compactly supported radial basis functions of minimal degree
description: scientific article; zbMATH DE number 1740122