通过矩阵 corona 问题研究切片全纯函数的 corona 问题
The Corona Problem for Slice Holomorphic Functions via the Matrix Corona Problem
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中文总结 AI 辅助
本文针对取值于任意 $n\geq2$ 的 Clifford 代数 $\mathbb R_n$ 的切片超全纯函数，通过结合矩阵版 corona 定理、Bezout 恒等式与 Carleson 型条件，提出新的切片乘积写法，通用证明了 corona 定理。
中文摘要 AI 辅助
本文以通用方式证明了切片超全纯函数的 corona 定理，该定理适用于取值于任意 $n\geq2$ 的 Clifford 代数 $\mathbb R_n$ 的函数。该通用证明基于矩阵版的 corona 定理，再利用矩阵的某些对称性来重构函数的值。关键思路是将函数代数、Bezout 恒等式与 Carleson 型条件相结合。所得结果依赖于一种新的切片乘积写法，该写法改进了标准方法，且适用于任意维度。
英文摘要
In this paper we prove the Corona theorem for slice hyperholomorphic functions in a general way that applies to functions with values in a Clifford algebra $\mathbb R_n$ for any $n\geq 2$. This general proof is based on a matrix version of Corona's theorem and then exploiting some symmetries of the matrices that allow to reconstruct the values of the functions. The crucial idea is to tie together the algebra of the functions, the Bezout identities and the Carleson-type conditions. The results we obtain rest on a new way of writing the slice product which improves the standard approach and which holds in general dimension.
