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 $H^2(D^n)$. 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 $H^2(D^n)$. By exploiting the structure of minimal representations we obtain an explicit co-rank formula for Rudin's quotient modules.