An Abstract Beurlings Theorem for Several Complex Variables II

TL;DR

This paper extends an abstract version of Beurling's theorem to describe all closed invariant subspaces in various Hilbert spaces of analytic functions in multiple complex variables, building on prior valuation algebra results.

Contribution

It applies an abstract Beurling's theorem to characterize invariant subspaces in several complex variables, advancing the understanding of Hilbert modules in this context.

Findings

Complete descriptions of closed invariant subspaces

Application of valuation Hilbert modules

Extension of Beurling's theorem to multiple variables

Abstract

In a previous paper, we presented an Abstract Beurling's Theorem for valuation Hilbert modules over valuation algebras. In this paper, we shall apply this theorem to obtain complete descriptions of the closed invariant subspaces of a number of Hilbert spaces of analytic functions in several complex variables.