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- Title
New fractal functions on the sphere.
- Authors
Akhtar, Md. Nasim; Prasad, M. Guru Prem; Navascués, M. A.; Mohapatra, R. N.
- Abstract
In this article, a family of continuous functions on the unit sphere S ⊆ R 3 is considered as a generalization of spherical harmonics. The family is fractalized using a linear and bounded operator of functions on the sphere. Particular values of the scale vector in the iterated function system (IFS) may yield classical functions system on the sphere. We have shown that for different values of the scale vector in the IFS, Bessel sequences, frames, and Riesz bases can be established for the space L 2 (S) of square integrable functions on the sphere.
- Subjects
SPHERES; OPERATOR functions; INTEGRABLE functions; SPHERICAL harmonics; LINEAR operators
- Publication
European Physical Journal: Special Topics, 2021, Vol 230, Issue 21/22, p3755
- ISSN
1951-6355
- Publication type
Article
- DOI
10.1140/epjs/s11734-021-00321-8