香蕉视频

Title:聽Weak Coherence Theorem and a new introductory approach to S.C.V.-Oka Theory, I , II. (suite)

Abstract:聽The solution of the big three problems (Approximation, Cousin I/II, Levi (Hartogs' inverse) summarized by Behnke-Thullen 1934 and solved by K. Oka (1936-'53) are the foundation of S.C.V. and complex geometry. Oka's theory lead to the Oka-Cartan-Serre Grauert's theory and then L^2-dbar theory of Hoermander. In the present lecture I will present yet another, simpler, easier approach based on ``Weak Coherent Theorem''. I present a complete self-contained treatment of those three problems just by convergent power series and Cousin's integral (half of Cauchy's integral) without making use of Weierstrass' Preparation Theorem or Cohomology theory nor L^2-dbar. In the course I will present a short simple proof of L. Schwartz's Finiteness Theorem in a bit generalized form.