Local fractal functions and function spaces

2013/09/01 by Peter Massopust, Massopust, Peter · 1 citation
Computer Science · Mathematics · #28A80 #37C70 #41A05 #41A30 #42B35 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Dynamics and Fractals #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1309.0243

openalex publication_date 2013/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce local iterated function systems and present some of their basic properties. A new class of local attractors of local iterated function systems, namely local fractal functions, is constructed. We derive formulas so that these local fractal functions become elements of various function spaces, such as the Lebesgue spaces L^p, the smoothness spaces Cⁿ, the homogeneous Hölder spaces C^s, and the Sobolev spaces W^m,p.

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• Semi-Rings, Semi-Vector Spaces, and Fractal Interpolation

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