On the zero sets of bounded holomorphic functions in the bidisc (Q2365023)

The following Rudin's theorem is well-known. If \(E\) is an analytic set in the polydisc \(D^n= \{z=(z_1, \dots, z_n)\), \(|z_i |<1\), \(1\leq i\leq n\}\) and the intersection of \(E\) with the neighbourhood of its frame is empty then \(E\) is the zero set of a bounded holomorphic function in \(D^n\) (counting multiplicity). The authors reprove this result in a constructive way. This method allows them to generalize this theorem and some of the P. S. Chee results.