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More General Fractal Functions on the Sphere

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Abstract

In this article, a family of continuous functions on the unit sphere \(S\subseteq \mathbb {R}^{3}\) generalizing the spherical harmonics, is considered. Using fractal methodology, the fractal version of this family of continuous functions on the sphere S is constructed. To do this, an iterated function system (IFS) and a linear bounded operator that maps classical functions to its fractal analogues is defined. Some approximation properties of fractal functions on the sphere are investigated. Restricting the scale vector involved in the IFS, a fractal Hilbert basis is established for the functions on the sphere.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Guwahati, Guwahati, Assam,  781039, India

    Md. Nasim Akhtar & M. Guru Prem Prasad

  2. Departamento de Matemática Aplicada, Universidad de Zaragoza, Saragossa, Spain

    M. A. Navascués

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  1. Md. Nasim Akhtar
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  2. M. Guru Prem Prasad
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  3. M. A. Navascués
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Correspondence to Md. Nasim Akhtar.

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Akhtar, M.N., Guru Prem Prasad, M. & Navascués, M.A. More General Fractal Functions on the Sphere. Mediterr. J. Math. 16, 134 (2019). https://doi.org/10.1007/s00009-019-1410-2

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  • DOI: https://doi.org/10.1007/s00009-019-1410-2

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