Study of multi-microlocalization and its applications

2017 Fiscal Year Final Research Report

• Project/Area Number: 15K04887
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Hokkaido University
• Principal Investigator: Honda Naofumi 北海道大学, 理学研究院, 教授 (00238817)
• Project Period (FY): 2015-04-01 – 2018-03-31
• Keywords: 超局所解析 / 多重特殊化

Outline of Final Research Achievements

Multi-microlocalization is a method which enables us to microlocalize an object along several manifolds simultaneously. The purpose of this research is to extend this mothod to more general cases, and then, to establish a theory of multi-microlocal operators.
In the first two years of our research, we studied generalization of multi-specialization and succeeded in constructing multi-specialization for a general family of submanifolds located suitably. During the rest of the period, we studied applications of Cech-Dolbeault cohomology theory to the theory of hyperfunctions. We had several interesting results, which suggested us that the theory is very effective for a construction of multi-microlocal operators too.

Free Research Field

代数解析