Wavelets on the 2-sphere: A group-theoretical approach (Q1818574)

In this paper the authors derive a continuous wavelet transform on the 2-dimensional sphere \(S^2\) using the square integrable group representation theory. The targeted group is the Lorentz group \(SO_0(3,1)\). Since its representation is not square integrable, the theory is restricted on a subgroup, namely the product \(SO(3)\) (the motions, or rotations) and \(R^{+}_{*}\) (the local dilations, acting on tangent space and pulled-back through the stereographic projection). Next, a necessary condition for admissibility is obtained, and, in the Euclidean limit (i.e., the sphere radius going to infinity) it becomes the usual zero mean necessary condition.