Studies on complex analysis for pseudoconvex domains of finite type

2014 Fiscal Year Final Research Report

• Project/Area Number: 22540199
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Kyushu University
• Principal Investigator: KAMIMOTO Joe 九州大学, 数理(科)学研究科(研究院), 准教授 (90301374)
• Research Collaborator: NOSE Toshihiro 九州産業大学, 工学部, 特認講師 (90637993)
• Project Period (FY): 2010-04-01 – 2015-03-31
• Keywords: 有限型擬凸領域 / 正則関数 / 境界挙動 / ピーク関数 / ベルグマン核 / 振動積分 / 局所ゼータ関数 / ニュートン多面体

Outline of Final Research Achievements

In the study of several complex variables, it is very important to understand the boundary behavior of holomorphic functions. I precisely studied this subject. In particular, I am interested in the case when the domain satisfies the finite type condition. In this investigation, the concept of Newton polyhedra, which is important in the study of singularity theory, reflects these investigations. On the other hands, I also study the asymptotic analysis of oscillatory integrals and local zeta functions, which are closely related to the above mentioned studies.

Free Research Field

多変数複素解析、　調和解析