Cauchy transform on nonrectifiable surfaces in Clifford analysis

Abstract:

The problem of reconstructing a monogenic Clifford algebra valued function on the boundary Γ of a general open set Ω in Rn + 1 from a prescribed jump data u over the boundary is deeply connected with the study of the Clifford-Cauchy transform(CΓ u) (x) : = under(∫, Γ) frac(over(y - x, -), σn | y - x |n + 1) n (y) u (y) d y, x ∉ Γ . Necessary and sufficient condition on non-rectifiable Γ is established guaranteeing the existence of continuous boundary values of this transform for all functions satisfying a Hölder type condition. © 2007 Elsevier Inc. All rights reserved.

Año de publicación:

2008

Keywords:

• Cauchy transform
• Rectifiability
• Clifford analysis

Fuente:

scopus