2017 Fiscal Year Final Research Report
Phase space analysis by modulation spaces
| Project/Area Number |
26610021
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Basic analysis
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| Research Institution | Nagoya University |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
TOMITA NAOHITO 大阪大学, 大学院理学研究科, 准教授 (10437337)
TERASAWA YUTAKA 名古屋大学, 大学院多元数理科学研究科, 准教授 (90546160)
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| Project Period (FY) |
2014-04-01 – 2018-03-31
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| Keywords | モジュレーション空間 / 相空間解析 / 正準変換 / 分散型方程式 / 非線形問題 |
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| Outline of Final Research Achievements |
We clarified the inclusion property between Wiener-amalgam spaces, which is defined in a similar way to modulation spaces, and Sobolev spaces. We also consider the application of modulation spaces to non-linear problems and discuss the local well-posedness of the Davey-Stewartson equation which describes a kind of water wave. In connection to it, we construct a theory of smoothing effect of non-dispersive equations. Furthermore, we gave an affirmative answer to the question “Does the composite function of a smooth function and a function in a modulation space belong to the same modulation space?”
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| Free Research Field |
偏微分方程式論
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