Invariant (fractal) vector measures as fixed points of Markov-type operators (Q2108943)
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scientific article; zbMATH DE number 7634839
| Language | Label | Description | Also known as |
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| English | Invariant (fractal) vector measures as fixed points of Markov-type operators |
scientific article; zbMATH DE number 7634839 |
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Invariant (fractal) vector measures as fixed points of Markov-type operators (English)
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20 December 2022
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The authors present a generalization of the theory of fractal invariant measures in the context of the Barnsley-Hutchinson setting of iterated function systems (IFSs). The discrete index in the definition of an IFS is replaced by a measurable function from a general measure space. The associated Markov operator is then seen to act on vector measures. Employing such concepts as sequilinear integrals, a Kantorovich-type metric and the Bochner integral, the authors derive the fixed points for this Markov operator which are vector-valued measures. Examples are also given.
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linear and continuous operator
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Bochner integral
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sesquilinear uniform integral
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measure of bounded variation
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Monge-Kantorovich norm and distance
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contraction principle
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fractal (invariant) measure
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