Real Harmonic Analysis on the Special Orthogonal Group

This paper presents theoretical analysis and software implementation for real harmonics on the special orthogonal group. Noncommutative harmonic complex-valued functions group has been studied extensively. However, it is customary to treat as a case of complex analysis, there have limited results developed specifically real-valued functions. Here, we develop set explicit formulas irreducible unitary representations group, provide several operational properties, such derivatives, sampling, Clebsch-Gordon coefficients. Furthermore, implement both into an open source package that utilizes parallel processing through OpenMP library. The efficacy presented are illustrated by benchmark studies application spherical shape matching.