# Spherical Continuous Wavelet Transforms arising from sections of the Lorentz group

Milton Ferreira

given at  strobl07 (18.06.07 16:15)
id:  563
length:  25min
status:  accepted
type:  talk
We consider the conformal group of the unit sphere $S^{n-1},$ the Lorentz group $Spin^+(1,n)$ (double covering group of the proper Lorentz group $SO_0(1,n)$) for the study of spherical continuous wavelet transforms (SCWT). The parameter space is determined by a factorization of the gyrogroup of the unit ball by an appropriate gyro-subgroup. We define admissible local and global sections and we study some families of sections that give rise to SCWT. These SCWT extend the SCWT of J.P. Antoine and P. Vandergheynst , which itself arises from the fundamental section of our homogeneous space.