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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>>