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arXiv 2202.02674math.CV
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Beurling定理在赋值Hilbert模与多复变量中的应用

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

Charles W. Neville

备注：
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_α$ 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
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AI总结：

本文发展赋值Hilbert模理论，证明Beurling定理版本，并应用于描述多复变量中多个解析函数Hilbert空间的闭不变子空间。

摘要：

我们发展了赋值Hilbert模理论，并证明了这些模的Beurling定理的一个版本。然后，我们将我们的Beurling定理版本应用于获得多复变量中若干解析函数Hilbert空间的闭不变子空间的完整描述，包括多圆盘、球和对称有界域的$H^2$空间，以及复解析流形上的加权$A^2$空间。

英文摘要：

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 $H^2$ of the polydisk the ball, and bounded symmetric domains, and weighted $A^2$ spaces on complex analytic manifolds.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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