| Budget Amount *help |
¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
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| Outline of Final Research Achievements |
The main idea of this research is the intimate relation between the smoothness of a function and the decay of its Fourier transform. We use the Weyl-Stone-Titchmarsh-Kodaira theorem on general expansions. The main subjects are as follows; (1) to give a generalization of the condition on associated density functions, (2) to consider the distribution of eigenvalues for the operators under consideration, and (3) to reconsider the problem in light of wavelet theory. One of the techniques is to give a weighted inequality in Besov spaces. This research comes from classical analysis, and an ability to use a classical method is essential. Such a collection of knowledge will become important in our future research.
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