Harmonic projection operators map square integrable functions on a sphere onto subspaces of spherical harmonics. Let Sdn−1 denote the unit sphere in ℝdn, with d∈{1,2,4,8}. In this paper, we start to study these projectors in the octonionic setting, that is, when d=8 and n=2. We also formulate a conjecture about the norm of harmonic projection operators, considered as operators from Lp(Sdn−1) onto L2(Sdn−1), for 1≤p≤2 and d∈{1,2,4,8}.
On Octonionic Harmonic Projection Operators
Casarino V.
2024
Abstract
Harmonic projection operators map square integrable functions on a sphere onto subspaces of spherical harmonics. Let Sdn−1 denote the unit sphere in ℝdn, with d∈{1,2,4,8}. In this paper, we start to study these projectors in the octonionic setting, that is, when d=8 and n=2. We also formulate a conjecture about the norm of harmonic projection operators, considered as operators from Lp(Sdn−1) onto L2(Sdn−1), for 1≤p≤2 and d∈{1,2,4,8}.
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