- The Cauchy transform
Steven R. Bell · 2015
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.