Spherical Mean On Metivier Groups And Uniqueness Results For Quaternion Weyl Transform

Abstract

In this thesis, the spherical mean of the metivier group is considered and we characterize the spherical harmonic coefficients of certain functions in terms of polynomial growth by which we infer a support theorem. Additionally we study the injectivity of the spherical mean for continuous functions in the metivier group. Further we study the boundedness and uniqueness of quanterion Weyl transform (QWT). Then we obtain an analogue of the benedicks Amrein-Berthier theorem for QWT.