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On Dimension of Fractal Functions on Product of the Sierpiński Gaskets and Associated Measures

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Abstract

In this article, our aim is to estimate the fractal dimensions of the graphs of fractal interpolation functions (FIFs) on the product of two Sierpiński gaskets. To achieve this, we employ the Hölder function spaces. We also define a fractal operator on Hölder spaces originated from the FIFs and establish some operator-theoretic properties such as bounded below and invariant subspaces of it. Additionally, we provide bounds on the Hausdorff dimensions of the invariant measures that are supported on the graphs of these FIFs.

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Funding

The second author is supported by the Analysis, Probability & Fractals Laboratory (No. LR18ES17). The third author is supported by the Ministry of Education (IIIT Allahabad, India) financially through his CPDA grant.

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Authors and Affiliations

  1. Department of Mathematics, Punjab Engineering College, Deemed to be University, Sector 12, Chandigarh, 160012, India

    Rattan Lal

  2. Analysis, Probability and Fractals Laboratory: LR18ES17, Department of Mathematics, Faculty of Sciences of Monastir, University of Monastir, 5000, Monastir, Tunisia

    Bilel Selmi

  3. Department of Applied Sciences, IIIT Allahabad, Prayagraj, 211015, India

    Saurabh Verma

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  1. Rattan Lal
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Correspondence to Bilel Selmi.

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Lal, R., Selmi, B. & Verma, S. On Dimension of Fractal Functions on Product of the Sierpiński Gaskets and Associated Measures. Results Math 79, 73 (2024). https://doi.org/10.1007/s00025-023-02108-w

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