Spherical Monogenic Functions and Analytic Functionals on the Unit Sphere

Abstract

The aim of this paper is to introduce the analogues of the restrictions of $z\to z^k$, $k\in\mathbf{Z}$, $z\in\mathbf{C}$, to the unit circle, in the case of the unit sphere $\partial B(0,1)$ in $\mathbf{R}^{m+1}$ and to apply them to boundary value problems of left monogenic functions in $\mathbf{R}^{m+1}\backslash \partial B(0,1)$.