Generalizaciones de las funciones inframonogénicas en el análisis de Clifford

Clifford analysis focuses in the so-called monogenic functions, which are recognized as natural generalizations of the holomorphic functions of the complex plane. Due to the non-commutativity of the product in Clifford algebras, the inframonogenic functions arise as a non-commutative version of the harmonic ones. The construction of Dirac operators with arbitrary orthonormal bases of makes possible the emergence of a new subclass of biharmonic functions that generalize to inframonogenic functions. In this work, a Cauchy integral formula and a jump problem for this type of functions will be discussed, as well as the connection with the Lamé-Navier system. At the end, well-posed boundary problems and Fischer decompositions for the polynomial space will be shown.