Approximate dimension applied to criteria for monogenicity on fractal domains

Abstract:

Suppose that Ω is a bounded domain of ℝn with a fractal boundary Γ and let ℝ0,n be the real Clifford algebra constructed over the quadratic space ℝn. Replacing the fractal dimensions of Γ with conditions of approximating character we will characterize the monogenicity of a ℝ0,n-valued function F in the interior and exterior of Ω, in terms of its boundary value f = F{pipe}Γ. Moreover, our geometric perspective allows for generalizations of certain two-sided monogenic extension results to a wide class of domains. © 2012 Sociedade Brasileira de Matemática.

Año de publicación:

2012

Keywords:

• Fractals
• jump problem
• Clifford analysis

Fuente:

scopus