Regresar

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 R<sup>m</sup> 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 R<sup>m</sup>. Moreover, we extend our results to the fractional context by means of the Caputo derivative and Weyl relations.