ABSTRACT
If u is a C∞ function defined on the boundary of a bounded domain Ω in the plane with C∞ smooth boundary, then the Cauchy transform of u is a holomorphic function Cu on Ω given by
(Cu)(z) = 1 2πi
∫ bΩ
u(ζ)
ζ − z dζ.
If u is a C∞ function defined on the boundary of a bounded domain Ω in the plane with C∞ smooth boundary, then the Cauchy transform of u is a holomorphic function Cu on Ω given by
(Cu)(z) = 1 2πi
∫ bΩ
u(ζ)
ζ − z dζ.