solidot新版网站常见问题,请点击这里查看。

A Remark on Oka's Coherence without Weierstrass' Preparation Theorem and the Oka Theory. (arXiv:1704.07726v1 [math.CV])

来源于:arXiv
The proofs of Oka's Coherence Theorems are based on Weierstrass' Preparation (division) Theorem. Here we observe that a Weak Coherence of Oka proved without Weierstrass' Preparation (division) Theorem, but only with \textit{power series expansions} is sufficient to prove Oka's J\^oku-Ik\^o and hence Cousin I, II, holomorphic extensions, and Levi's Problem, as far as the domain spaces are non-singular. The proof of the Weak Coherence of Oka is almost of linear algebra. We will present some new or simplified arguments in the proofs. 查看全文>>