Dissertation/Thesis Abstract

Holomorphically parametrized L2 Cramer's rule and its algebraic geometric applications
by Sung, Yih, Ph.D., Harvard University, 2013, 108; 3567083
Abstract (Summary)

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.

Indexing (document details)
Advisor: Siu, Yum-Tong
Commitee: Harris, Joe, Siu, Yum-Tong, Taubes, Clifford
School: Harvard University
Department: Mathematics
School Location: United States -- Massachusetts
Source: DAI-B 74/10(E), Dissertation Abstracts International
Subjects: Mathematics
Keywords: Cramer's rule, Division theorem, L2 method
Publication Number: 3567083
ISBN: 978-1-303-18719-3
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