TY - JOUR
T1 - Approximate dimension applied to criteria for monogenicity on fractal domains
AU - Abreu-Blaya, Ricardo
AU - Bory-Reyes, Juan
AU - Kats, Boris A.
N1 - Funding Information:
or, equivalently, f (x) = Ψ∗ f (x). In view of the assumption made, we thus obtain that f (x) = f Ψ∗(x). The two-sided monogenicity of F in Ω is now implied by Theorem 3. □ Acknowledgments. The final version of the paper was written when the first two authors were visiting the IMPA, Rio de Janeiro in the spring of 2011; the financial support and kind hospitality are gratefully acknowledged. The third author is supported by Russian Foundation for Basic Researches, grants 09-01-12188-ofi-m and 10-01-00076-a.
PY - 2012/12
Y1 - 2012/12
N2 - 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.
AB - 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.
KW - Clifford analysis
KW - fractals
KW - jump problem
UR - http://www.scopus.com/inward/record.url?scp=84869144175&partnerID=8YFLogxK
U2 - 10.1007/s00574-012-0025-z
DO - 10.1007/s00574-012-0025-z
M3 - Artículo
SN - 1678-7544
VL - 43
SP - 529
EP - 544
JO - Bulletin of the Brazilian Mathematical Society
JF - Bulletin of the Brazilian Mathematical Society
IS - 4
ER -