Discrete Hypercomplex Function Theory and its Applications

Recently, one can observe an increased interest in discrete function theories and their applications. Although we will give a broader overview in our talk we would like to give a closer idea on the topic and its applications. To this end we present the question of boundary values of discrete monogenic functions in this short text. We also show their applicability in the theory of discrete Riemann boundary value problems (Riemann BVP's). The grid itself was chosen in view of applications to image processing, such as discrete monogenic functions.