Rado's theorem for factorisations of the Laplace operator (Q1953992)

Let \(\widehat{D}\) and \(D\) be a pair of first order differential operators with constant coefficients such that the product \(\widehat{D} D\) is equal to the Laplace operator. A classical theorem of Tibor Radó states that if a function \(h\) is continuous on an open set \(\Omega\subset \mathbb{C}^n\) and holomorphic on the complement of its zero locus, then it is holomorphic everywhere on \(\Omega\). This paper extends this classical result by substituting the holomorphicity of \(h\) with the assumptions that \(Dh\) vanishes.