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
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2014: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2013: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| 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 / ウィーナーアマルガム空間 / フーリエ・ルベーグ空間 / 波束変換 / 波面集合 / ウィナーアマルガム空間 |
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| 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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Report
(4 results)
Research Products
(13 results)
