Converse of Cauchy's theorem: if f is continuous on an open set Ω and its integral around every triangle contained in Ω is zero, then f is holomorphic on Ω. Used to prove holomorphy of limits (Montel) and of Fourier transforms. Morera…
Converse of Cauchy's theorem: if f is continuous on an open set Ω and its integral around every triangle contained in Ω is zero, then f is holomorphic on Ω. Used to prove holomorphy of limits (Montel) and of Fourier transforms. Morera…