Submodules of the Hardy space over polynomial algebras

Marc J. Jaffrey, Timothy L. Lance and Michael I. Stessin

Vol. 194 (2000), No. 2, 373–392

DOI: 10.2140/pjm.2000.194.373

Abstract

The classical Hardy space H² has a natural structure of a module over the algebra of polynomials ℂ[z]. In this setting the theorem of Beurling describes all closed ℂ[z]-submodules of H². In this paper we prove a Beurling-type theorem for H² as a module over a finitely generated polynomial algebra.

Milestones

Received: 14 July 1998

Revised: 28 June 1999

Published: 1 June 2000