The isotonic Cauchy transform

Abstract:

Starting with an integral representation for the class of continuously differentiable solutions f : ℝ²ⁿ, → ℂ<inf>0,n</inf> of the system ∂x<inf>1</inf> f + if̃∂x<inf>2</inf> = 0 where ℂ<inf>0,n</inf> is the complex Clifford algebra constructed over ℝⁿ, x<inf>1</inf>, x<inf>2</inf> are some suitable Clifford vectors and ∂<inf>x1</inf>, ∂x<inf>2</inf> their corresponding Dirac operators, we define the isotonic Cauchy transform and establish the Sokhotski-Plemelj formulae. Some consequences of this result are also derived. © Birkhäuser Verlag Basel/Switzerland 2007.

Año de publicación:

2007

Keywords:

• Sokhotski-plemelj formulae
• Clifford analysis
• Isotonic functions

Fuente:

scopus