Self-similar vector measures of Markov-type operators

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.