Star-generating vectors of Rudin's quotient modules

The purpose of this paper is to study a class of quotient modules of the Hardy module H2(Dn)H2(Dn). Along with the two variables quotient modules introduced by W. Rudin, we introduce and study a large class of quotient modules, namely Rudin's quotient modules of H2(Dn)H2(Dn). By exploiting the structure of minimal representations we obtain an explicit co-rank formula for Rudin's quotient modules.