2014 Fiscal Year Final Research Report
Partial differential equations and modulation spaces
| Project/Area Number |
24740092
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Basic analysis
|
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| Research Institution | Yamagata University |
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Principal Investigator |
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| Project Period (FY) |
2012-04-01 – 2015-03-31
|
| Keywords | モジュレーション空間 / ウィーナー・アマルガム空間 / 関数空間 / シュレディンガー方程式 |
|---|
| Outline of Final Research Achievements |
We introduce a new representation of the Schr\"odinger operators of a free particle and a harmonic oscillator by using the short time Fourier transform. As applications, we give new estimates for the solution to the Schr\"odinger equation with quadratic and sub-quadratic potentials in the framework of modulation spaces. We also characterize the Fourier-Lebesgue type wave front set by using the wave packet transform.
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| Free Research Field |
数物系科学
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