| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Outline of Final Research Achievements |
Concerning non-commutative Fourier transforms, we studied two examples of exponential solvable Lie groups; for them we described the images of their C*-algebras by the Fourier transform in terms of the orbit method. For the norm of the Lp-Fourier transform (1<p<2), we treated a semi-direct product group of a unimodular type I Lie group N and a compact group acting on N, and we obtained an estimate of the norm of its Lp-Fourier transform by using that of N.
For holomorphically induced representations, we studied a semi-direct product group G of a vector group Rn and R acting on Rn. Assuming that there is a complex one dimensional subalgebra h such that the space h+h~, where h~ is the complex conjugate of h, generates the complexification of the Lie algebra of G and that G satisfies some technical conditions, we obtained a non-zero representation holomorphically induced from h, and its decomposition into a direct integral of irreducible representations.
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