https://doi.org/10.1140/epjs/s11734-021-00321-8
Regular Article
New fractal functions on the sphere
1
Department of Mathematics, Presidency University, 86/1, College Street, 700 073, Kolkata, India
2
Department of Mathematics, Indian Institute of Technology Guwahati, 781039, Guwahati, Assam, India
3
Departamento de Matemática Aplicada, Universidad de Zaragoza, Zaragoza, Spain
4
Department of Mathematics, University of Central Florida, 4393 Andromeda Loop, 32816, Orlando, FL, USA
Received:
25
June
2021
Accepted:
25
October
2021
Published online:
1
December
2021
In this article, a family of continuous functions on the unit sphere 
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 
of square integrable functions on the sphere.
© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2021
