More General Fractal Functions on the Sphere

  • Md. Nasim AkhtarEmail author
  • M. Guru Prem Prasad
  • M. A. Navascués


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.


Fractal interpolation functions \(\alpha \)-fractal interpolation functions spherical harmonics best approximations Hilbert bases 

Mathematics Subject Classification

Primary 43A90 33C55 Secondary 28A80 



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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Md. Nasim Akhtar
    • 1
    Email author
  • M. Guru Prem Prasad
    • 1
  • M. A. Navascués
    • 2
  1. 1.Department of MathematicsIndian Institute of Technology GuwahatiGuwahatiIndia
  2. 2.Departamento de Matemática AplicadaUniversidad de ZaragozaSaragossaSpain

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