Self-similar vector measures of Markov-type operators

TL;DR

This paper introduces a framework for constructing self-similar vector measures as fixed points of Markov-type operators derived from iterated function systems and linear operators on Hilbert spaces, generalizing classic measures.

Contribution

It extends the concept of self-similar measures to vector measures using Markov-type operators associated with iterated function systems.

Findings

Existence of fixed points under certain conditions

Construction of concrete models with computations

Generalization of Hutchinson measures

Abstract

We consider iterated function systems (finite or countable), together with linear and continuous operators on Hilbert spaces, which enable us to construct Markov-type operators. Under suitable conditions, these Markov-type operators have fixed points, which are self-similar (invariant) vector measures, thus generalizing the classic Hutchinson self-similar measures. Several models with concrete computations are introduced.