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.
Logarithmic derivative of the Euler Γ function in Clifford analysis.
The logarithmic derivative of the Γ-function, namely the ψ-function, has numerous applications. We define analogous functions in a four dimensional space. We cut lattices and obtain Clifford-valued functions. These functions are holomorphic cliffordian and have similar properties as the ψ-function. These new functions show links between well-known constants: the Eurler gamma constant and some generalisations, ζ(2), ζ(3). We get also the Riemann zeta function and the Epstein zeta functions.
Analytic Cliffordian functions.
The Legendre Formula in Clifford Analysis
2000 Mathematics Subject Classification: 30A05, 33E05, 30G30, 30G35, 33E20. Let R0,2m+1 be the Clifford algebra of the antieuclidean 2m+1 dimensional space. The elliptic Cliffordian functions may be generated by the z2m+2 function, analogous to the well-known Weierstrass z-function. The latter satisfies a Legendre equality. We prove a corresponding formula at the level of the monogenic function Dm z2m+2.
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