The orthogonal decomposition of Banach spaces and its applications

2017 Fiscal Year Final Research Report

• Project/Area Number: 25400124
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Iwate University
• Principal Investigator: Honda Takashi 岩手大学, 教育学部, 准教授 (30633531)
• Co-Investigator(Kenkyū-buntansha): 川田 浩一 岩手大学, 教育学部, 教授 (70271830)
• Co-Investigator(Renkei-kenkyūsha): IWATA Yukiko 東北学院大学, 教養学部, 准教授 (60466456)
• Research Collaborator: KAMINO Shogo
• Project Period (FY): 2013-04-01 – 2018-03-31
• Keywords: バナッハ空間 / 解析的数論 / 直交補空間分解 / 線形射影 / ゴールドバッハの予想

Outline of Final Research Achievements

This research is based on the extension of the orthogonal decomposition of a Hilbert space to a Banach space which was showed by Prof. Takahashi and us. In this research, we showed the condition of retracts onto which the images of linear contractive projections which map the whole space converges. A linear contractive projection in a Banach space is applied to probability theory as a conditional expectation. The behavior of a distribution induced by a stochastically perturbed dynamical system is represented as a semigroup of contractive linear operator on a Banach space. We and Prof. Iwata obtain results concerned with the behavior of a distribution induced by a stochastically perturbed dynamical system and they are published in "Springer Proceedings in Mathematics & Statistics". We also obatin results about Goldbach's conjecture in analytic number theory.

Free Research Field

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