TY - JOUR
T1 - A jump problem for β-analytic functions in domains with fractal boundaries
AU - Abreu-Blaya, Ricardo
AU - Bory-Reyes, Juan
AU - Vilaire, Jean Marie
PY - 2010/1
Y1 - 2010/1
N2 - Let γ be a simple closed Jordan curve in the complex plane ℂ, ω+ and ω- the corresponding domains in ℂ, with 0 ε ω+ and ∞ ε ω-. The classes of complex valued functions satisfying some boundary conditions as well as integral representations for them are considered. Main goal of this paper is the study of the standard jump Riemann boundary value problem over a fractal curve γ (ℓ+{t) - ℓ- (t) = f(t), t ε γ, where ℓ ±(t) are the boundary values of the β-analytic function ℓ at the point t, approaching the boundary from ω+ and ω,- respectively.
AB - Let γ be a simple closed Jordan curve in the complex plane ℂ, ω+ and ω- the corresponding domains in ℂ, with 0 ε ω+ and ∞ ε ω-. The classes of complex valued functions satisfying some boundary conditions as well as integral representations for them are considered. Main goal of this paper is the study of the standard jump Riemann boundary value problem over a fractal curve γ (ℓ+{t) - ℓ- (t) = f(t), t ε γ, where ℓ ±(t) are the boundary values of the β-analytic function ℓ at the point t, approaching the boundary from ω+ and ω,- respectively.
KW - -analytic functions
KW - Fractals
KW - Jump problem
KW - β
UR - http://www.scopus.com/inward/record.url?scp=77956652735&partnerID=8YFLogxK
U2 - 10.1007/s13163-009-0002-2
DO - 10.1007/s13163-009-0002-2
M3 - Artículo
SN - 1139-1138
VL - 23
SP - 105
EP - 111
JO - Revista Matematica Complutense
JF - Revista Matematica Complutense
IS - 1
ER -