Holomorphic Cliffordian Product

Guy Laville (1)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme

Let R_{0,n} be the Clifford algebra of the antieuclidean vector space of dimension n. The aim is to built a function theory analogous to the one in the C case. In the latter case, the product of two holomorphic functions is holomorphic, this fact is, of course, of paramount importance. Then it is necessary to define a product for functions in the Clifford context. But, non-commutativity is inconciliable with product of functions. Here we introduce a product which is commutative and we compute some examples explicitely.

Mots clés: Non-commutative analysis; Clifford algebra; symmetric algebra; Clifford analysis; product; holomorphic Cliffordian functions

Domaines: Variables complexes [math.CV]

Guy Laville. Holomorphic Cliffordian Product. 2005. ⟨hal-00003227⟩