An application of functional equations for generating ε-invariant measures

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:476

Article

Morawiec, Janusz¹  Zurcher, Thomas¹ 

[1] Uniwersytet Slaski, Inst Matemat, Bankowa 14, PL-40007 Katowice, Poland

关键词: Markov operators;    epsilon-invariant measures;    Functional equations;    Integrable solutions;    Iterated function system;   

DOI  :  10.1016/j.jmaa.2019.04.013

来源: Elsevier

【 摘 要 】

Let (X, A, mu) be a probability space and let S: X -> X be a measurable transformation. Motivated by K. Nikodem's paper from 1991 published in the Czechoslovak Mathematical Journal [7], we concentrate on a functional equation generating measures that are absolutely continuous with respect to mu and epsilon-invariant under S. As a consequence of the investigation, we obtain a result on the existence and uniqueness of solutions phi is an element of L-1([0,1]) of the functional equation phi(x) = Sigma(N)(n=1) vertical bar f(n)'(x)vertical bar phi(f(n)(x))+ g(x), where g is an element of L-1([0, 1]) and f(1), ..., f(N) : [0,1] -> [0,1] are functions satisfying some extra conditions. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free