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Holomorphic Cliffordian Product
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
Stone-Weierstrass Theorem
It will be shown that the Stone-Weierstrass theorem for Clifford-valued
functions is true for the case of even dimension. It remains valid for the odd
dimension if we add a stability condition by principal automorphism
Analytic cliffordian functions
In classical function theory, a function is holomorphic if and only if it is
complex analytic. For higher dimensional spaces it is natural to work in the
context of Clifford algebras. The structures of these algebras depend on the
parity of the dimension n of the underlying vector space. The theory of
holomorphic Cliffordian functions reflects this dependence. In the case of odd
n the space of functions is defined by an operator (the Cauchy-Riemann
equation) but not in the case of even . For all dimensions the powers of
identity (z^n, x^n) are the foundation of function theory
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