Linear quasi-metric and sequence representation of Shepp space
| Project/Area Number |
26400155
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Multi-year Fund |
|---|
| Section | 一般 |
|---|
| Research Field |
Basic analysis
|
|---|
| Research Institution | Fuzzy Logic Systems Institute |
|---|
Principal Investigator |
Okazaki Yoshiaki 一般財団法人ファジィシステム研究所, 研究部, 特別研究員 (40037297)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
本田 あおい 九州工業大学, 大学院情報工学研究院, 准教授 (50271119)
|
|---|
| Research Collaborator |
SATO Hiroshi
|
|---|
| Project Period (FY) |
2014-04-01 – 2017-03-31
|
| Project Status |
Completed (Fiscal Year 2016)
|
| 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)
|
|---|
| Keywords | 準距離 / Shepp 空間 / 関数空間 / Lp 空間 / 非加法的集合関数 / 数列空間 / フーリエ変換 / doubling condition / 位相線形空間 / 非加法的単調集合関数 / ファジィ測度 / 可測関数 / r階 Shepp 空間 / 距離付け定理 / Banach 空間 / doubling dimension |
|---|
| 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.
|
Report
(4 results)
Research Products
(21 results)
-
-
-
-
-
[Presentation] 包除積分の非離散化2017
Author(s)
(a)本田あおい，(b)岡崎悦明
Organizer
2017年 日本数学会年会 実函数論分科会
Place of Presentation
首都大学東京南大沢キャンパス（東京都 八王子市）
Year and Date
2017-03-24
Related Report
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
