Zeros of generalized holomorphic functions (Q863497)

It is proved that if the zero set of a Colombeau generalized function \(f\) is of positive measure, then \(f\) is zero. Using analogous methods, a more precise result is proved, and that result implies that if two holomorphic generalized functions take the same values on all points of a line, then they are equal. Throughout this paper, the main technical tools are the use of Blaschke products and the Poisson kernel for harmonic functions. The paper ends with proposing further open questions.