SUMMARY
Hyperbolic harmonics are hypothesized to be associated with the algebra so(2,1), analogous to how spherical harmonics relate to so(3). However, there is a lack of references or established literature confirming their existence. The discussion highlights the need for further exploration into the mathematical framework surrounding hyperbolic harmonics and their potential applications. The inquiry points to a gap in current mathematical resources regarding this topic.
PREREQUISITES
- Understanding of algebra so(3) and its relation to spherical harmonics.
- Familiarity with algebra so(2,1) and its mathematical implications.
- Knowledge of harmonic analysis and its applications in physics.
- Basic comprehension of non-compact groups in mathematical physics.
NEXT STEPS
- Research the mathematical properties of hyperbolic harmonics and their potential definitions.
- Explore the connections between algebra so(2,1) and hyperbolic geometry.
- Investigate existing literature on non-compact groups and their representations.
- Examine applications of spherical harmonics in physics to draw parallels with potential hyperbolic harmonics.
USEFUL FOR
Mathematicians, physicists, and researchers interested in advanced harmonic analysis, particularly those exploring the relationships between different algebraic structures and their applications in theoretical physics.