A jump problem for beta-analytic functions in domains with fractal boundaries

作者：Abreu Blaya Ricardo; Bory Reyes Juan; Vilaire Jean Marie^*

来源：Revista Matematica Complutense, 2010, 23(1): 105-111.

DOI：10.1007/s13163-009-0002-2

• beta-analytic functions
• Jump problem
• Fractals

Let gamma be a simple closed Jordan curve in the complex plane C, Omega(+) and Omega(-) the corresponding domains in C, with 0 is an element of Omega(+) and infinity is an element of Omega(-).
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 gamma
phi(+)(t) - phi(-)(t) = f(t), t is an element of gamma,
where phi(+/-)(t) are the boundary values of the beta-analytic function phi at the point t, approaching the boundary from Omega(+) and Omega(-) respectively.

• 出版日期2010-1