Suppose f,g1,[special characters omitted] ,gp are holomorphic functions over Ω ⊂ [special characters omitted]n. Then there raises a natural question: when can we find holomorphic functions h1, [special characters omitted] , hp such that f = Σg jhj? The celebrated Skoda theorem solves this question and gives a L2 sufficient condition. In general, we can consider the vector bundle case, i.e. to determine the sufficient condition of solving fi(x) = Σ gij(x)h j(x) with parameter x ∈ Ω. Since the problem is related to solving linear equations, the answer naturally connects to the Cramer's rule. In the first part we will give a proof of division theorem by projectivization technique and study the generalized fundamental inequalities. In the second part we will apply the skills and the results of the division theorems to show some applications.
|Commitee:||Harris, Joe, Siu, Yum-Tong, Taubes, Clifford|
|School Location:||United States -- Massachusetts|
|Source:||DAI-B 74/10(E), Dissertation Abstracts International|
|Keywords:||Cramer's rule, Division theorem, L2 method|
Copyright in each Dissertation and Thesis is retained by the author. All Rights Reserved
The supplemental file or files you are about to download were provided to ProQuest by the author as part of a
dissertation or thesis. The supplemental files are provided "AS IS" without warranty. ProQuest is not responsible for the
content, format or impact on the supplemental file(s) on our system. in some cases, the file type may be unknown or
may be a .exe file. We recommend caution as you open such files.
Copyright of the original materials contained in the supplemental file is retained by the author and your access to the
supplemental files is subject to the ProQuest Terms and Conditions of use.
Depending on the size of the file(s) you are downloading, the system may take some time to download them. Please be