- TL;DR Summary
- Real differentiability with complex variables.
In defining the Wirtinger (aka Cauchy-Riemann) linear operators, often used in signal analysis and in proofs of complex derivatives and the Cauchy-Riemann equations, one assumes differentiability in the real sense. This assumption is usually seen as obvious in the complex analysis setting since holomorphic functions must be smooth but I wonder if there's any circumstance in complex analysis in which real differentiability is not automatic for a complex variable function. There are plenty of complex functions of a complex variable that are not holomorphic but I can't think of examples that are not real differentiable.