Fractional Fischer decompositions by inframonogenic functions

Abstract

Inframonogenic functions can be viewed as a non-commutative version of the more traditional harmonic functions. In this paper we obtain a new Fischer decomposition for homogeneous polynomials in Rm in terms of (φ,ψ)-inframonogenic homogeneous polynomials. The latter being a natural generalization arising when structural sets φ, ψ are considered instead of the standard orthonormal basis of Rm. Moreover, we extend our results to the fractional context by means of the Caputo derivative and Weyl relations.