Beurling's Theorem for Valuation Hilbert Modules and Several Complex Variables
Abstract
We develop a theory of Valuation Hilbert Modules and prove a version of Beurling's theorem for these. Then we apply our version of Beurling's theorem to obtain complete descriptions of the closed invariant subspaces of a number of Hilbert spaces of analytic functions in several complex variables, including of the polydisk the ball, and bounded symmetric domains, and weighted spaces on complex analytic manifolds.
Cite
@article{arxiv.2202.02674,
title = {Beurling's Theorem for Valuation Hilbert Modules and Several Complex Variables},
author = {Charles W. Neville},
journal= {arXiv preprint arXiv:2202.02674},
year = {2023}
}
Comments
31 pages. Changed some terminology and added material on $R_1$ inner functions. v3: Added additional matrial on $ R_1 $ inner functions and their relation to $ A^p_\alpha $ inner functions. v4 : Revised terminology for valuation Hilbert modules. Added complete proofs of the Minimum Value Theorem, and the 4th Projection Lemma, plus other additions and corrections. arXiv admin note: text overlap with arXiv:2109.00695, arXiv:2108.12272