Linear quasi-metric and sequence representation of Shepp space

2016 Fiscal Year Final Research Report

• 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)
• Research Collaborator: SATO Hiroshi
• Project Period (FY): 2014-04-01 – 2017-03-31
• 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

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.

Free Research Field

実解析学，関数解析学，ファジィ測度論，確率論