A Martinelli-Bochner formula on fractal domains

Abstract:

A new perspective on a Cauchy integral formula for Clifford algebras valued functions on domains with quite smooth boundaries was discussed in [5]. On the other hand, the Cauchy transform associated to Clifford analysis has been involved recently with fractional metric dimensions and fractals, see [1, 2, 3]. In this paper we consider the question of possible generalizations of the Cauchy integral formula to domains with fractal boundary. As an application, we prove a Martinelli-Bochner type formula for several complex variables on such pathological domains. The proof makes heavy use of the isotonic approach of the monogenic functions theory. © 2009 Birkhäuser Verlag Basel/Switzerland.

Año de publicación:

2009

Keywords:

• Fractals
• Martinelli-Bochner formula
• Clifford analysis

Fuente:

scopus