The isotonic Cauchy transform

Abstract:

Starting with an integral representation for the class of continuously differentiable solutions f : ℝ2n, → ℂ0,n of the system ∂x1 f + if̃∂x2 = 0 where ℂ0,n is the complex Clifford algebra constructed over ℝn, x1, x2 are some suitable Clifford vectors and ∂x1, ∂x2 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