| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Outline of Final Research Achievements |
The Shepp space defined by an Lp function f is investigated. In the case of p=2, the inner and the outer approximation sequence spaces are introduced and the necessary and sufficient condition under which these two spaces are identical is given in terms of doubling condition of the functional of the Fourier transform of f. So that the sequence representation of the Shepp space is obtained. Further extensions to the Shepp space of order r>1 are studied.
As a natural extension of the Shepp space, the quasi-metric space with the linear structure is considered. We found many new and interesting examples of linear quasi-metric spaces constructing the Lp like spaces with respect to the non-additive set function (fuzzy measure). The new development of the linear quasi-metric space is expected hereafter.
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