Fractional divisibility of spheres with partially generic sets of rotations
Abstract
We say that an r-tuple (γ1,…,γr) of special orthogonal d×d matrices fractionally divides the (d−1)-dimensional sphere Sd−1 if there is a non-constant function f∈L2(Sd−1) such that its translations by γ1,…,γr sum to the constant-1 function. Our main result shows, informally speaking, that fractional divisibility is impossible if at least r/2 rotations are “generic”.
Fields of Study & Subjects
Structural Analysis and Optimization
Mathematics and Applications
Advanced Materials and Mechanics
Publication details
- Journal / source
- Fundamenta Mathematicae
- Publisher
- Institute of Mathematics, Polish Academy of Sciences
- Publication date
- 22 July 2026
- Language
- EN