English

Doubly commuting submodules of the Hardy module over polydiscs

Functional Analysis 2013-09-24 v3 Complex Variables Operator Algebras

Abstract

In this note we establish a vector-valued version of Beurling's Theorem (the Lax-Halmos Theorem) for the polydisc. As an application of the main result, we provide necessary and sufficient conditions for the completion problem in H(Dn)H^\infty(\mathbb{D}^n).

Keywords

Cite

@article{arxiv.1302.5312,
  title  = {Doubly commuting submodules of the Hardy module over polydiscs},
  author = {Jaydeb Sarkar and Amol Sasane and Brett D. Wick},
  journal= {arXiv preprint arXiv:1302.5312},
  year   = {2013}
}

Comments

14 pages, revised, to appear in Studia Mathematica

R2 v1 2026-06-21T23:30:12.484Z