Equivalence of Quotient Hilbert Modules

Proceedings Mathematical Sciences

Gadadhar Misra¹  Ronald G Douglas² 

[1] Indian Statistical Institute, R.V. College Post, Bangalore 0 0, India$$;Texas A&M University, College Station, Texas , USA$$

关键词: Hilbert modules;    function algebra;    quotient module;    longitudinal and transversal curvature;    kernel function;    jet and angle.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

Let $mathcal{M}$ be a Hilbert module of holomorphic functions over a natural function algebra $mathcal{A}(𝛺)$, where $𝛺 subseteq mathbb{C}^m$ is a bounded domain. Let $mathcal{M}_0 subseteq mathcal{M}$ be the submodule of functions vanishing to order 𝑘 on a hypersurface $mathcal{Z} subseteq 𝛺$. We describe a method, which in principle may be used, to construct a set of complete unitary invariants for quotient modules $mathcal{Q} = mathcal{M} ominus mathcal{M}_0$. The invariants are given explicitly in the particular case of 𝑘 = 2.

【 授权许可】

Unknown