| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2019: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2018: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2017: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| Outline of Final Research Achievements |
At the beginning, the purpose of our research was to study the detailed geometric and analytical structure of the fundamental solution to the Schroedinger equation on symmetric spaces.However, through the analysis of zonal spherical functions on symmetric spaces,we found that our research is closely related to the study of the operator theoretical property of mean value operators on symmetric spaces.Therefore, we decided to focus on this subject. The result we obtained in our research program is as follows.
We consider the mean value operator to be a map from the space of smooth functions to itself. Then we proved that the mean value operator is surjective under some suitable conditions.We also obtained some related results on convolution operators.It is expected that our result will be applied to the wave equations on symmetric spaces.
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