Star-Generating Vectors of Rudin's Quotient Modules

TL;DR

This paper investigates a broad class of quotient modules of the Hardy space on the polydisc, providing explicit formulas for their structure and co-rank, extending Rudin's original two-variable modules.

Contribution

It introduces and analyzes a large class of Rudin's quotient modules of H^2(D^n), including explicit co-rank formulas, expanding the understanding of their structure.

Findings

Derived explicit co-rank formulas for Rudin's quotient modules

Extended Rudin's two-variable modules to higher dimensions

Provided structural insights into minimal representations

Abstract

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.