| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Fiscal Year 2012: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Outline of Final Research Achievements |
I have researched methods of construction of the fundamental solution for heat equations corresponding to various kinds of subelliptic operators. This research is applicable to analyze both eigenvalues of operators and singularity of spectral zeta functions of subelliptic operators. Objects subelliptic operators of my research are the Fokker-Planck operator, subelliptic operators on spheres, operators on Nilpotent Lie groups.
In addition to this kind research I succeded to get the precise expression of the fundamental solution to degenerate elliptic operators, which are called operators of Grushin type. This study depends on theories of the modified Bessel functions. I show this method is also useful to study of Kohn-Laplacian which is deeply interested in complex analysis.
These results are published in six papers during the term of this aid.
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