Construction of quantitative methodology in phase space analysis

2014 Fiscal Year Final Research Report

• Project/Area Number: 23654049
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Basic analysis
• Research Institution: Nagoya University
• Principal Investigator: SUGIMOTO Mitsuru 名古屋大学, 多元数理科学研究科, 教授 (60196756)
• Co-Investigator(Renkei-kenkyūsha): TOMITA Naohito 大阪大学, 大学院理学研究科, 准教授 (10437337)
• Project Period (FY): 2011-04-28 – 2015-03-31
• Keywords: 相空間解析 / フーリエ積分作用素 / モジュレーション空間 / 時空間評価式 / 分散型方程式 / シュレディンガー方程式

Outline of Final Research Achievements

The objective of this research project was to establish a new and comprehensive methodology to deduce quantitative information of solutions to partial differential equations through phase space analysis, and as a fundamental subject we first prepared theoretical tools for the purpose, then we further applied them to various problems of partial differential equations. In particular we successfully got remarkable outcome on “fundamental theory of modulation spaces and its application”, “boundedness of Fourier integral property” and “smoothing estimates for dispersive equations”. During the research period, we organize various kind of international workshops aiming academic interaction between partial differential equations and harmonic analysis, and they resulted in great success in international human exchange.

Free Research Field

偏微分方程式論