Beurling's Theorem for Valuation Hilbert Modules and Several Complex Variables

2022/02/06 by Charles W. Neville, Neville, Charles W.
Mathematics · #32A36 #32A38 (Primary) 32A35 #46E20 (Secondary) #Complex Variables (math.CV) #FOS: Mathematics #Geometry and complex manifolds #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2202.02674

openalex publication_date 2022/02/06 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28

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 H² of the polydisk the ball, and bounded symmetric domains, and weighted A² spaces on complex analytic manifolds.

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