The orthogonal decomposition of Banach spaces and its applications

• 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
• Project Status: Completed (Fiscal Year 2017)
• Budget Amount: ¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000); Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
• 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 / 関数解析 / 作用素論 / 非線形関数解析

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.

Research Products

• [Journal Article] Operator Theoretic Phenomena of the Markov Operators which are Induced by Stochastic Difference Equations (2017)
  • Author(s): Takashi Honda and Yukiko Iwata
  • Journal Title: Springer Proceedings in Mathematics & Statistics Volume: 212 Pages: 125-135
  • DOI: 10.1007/978-981-10-6409-8_7
  • ISBN: 9789811064081, 9789811064098
  • Peer Reviewed
• [Journal Article] 3つの素数の3乗の和の話 (2017)
  • Author(s): 川田浩一
  • Journal Title: 数学セミナー Volume: 2017年6月号 Pages: 42-47
  • NAID: 40021211740
• [Journal Article] ゴールドバッハ予想と円周法 (2017)
  • Author(s): 川田浩一
  • Journal Title: 数理科学 Volume: 2017年9月号 Pages: 51-57
• [Journal Article] Goldbach問題 --- 3つの素数の和について (2016)
  • Author(s): 川田浩一
  • Journal Title: 京都大学数理解析研究所講 究録別冊 Volume: B53 Pages: 251-278
  • Peer Reviewed
• [Journal Article] Convergence theorems of linear contractive projections in Banach spaces (2016)
  • Author(s): Takashi Honda and Shogo Kamino
  • Journal Title: Proceedings of The Ninth International Conference on Nonlinear Analysis and Convex Analysis Volume: 9 Pages: 131-141
  • Peer Reviewed / Acknowledgement Compliant
• [Presentation] Some decomposition theorems of semigroups of linear contractive operators on Banach spaces (2016)
  • Author(s): Takashi Honda
  • Organizer: The fifth Asian conference on Nonlinear Analysis and Optimization (NAO-Asia 2016)
  • Place of Presentation: ときメッセ（新潟市）
  • Year and Date: 2016-08-01
  • Int'l Joint Research
• [Presentation] Operator theoretic phenomena of the Markov operators which are induced by stochastic difference equations (2016)
  • Author(s): Takashi Honda, Yukiko Iwata
  • Organizer: The 22nd International Conference on Difference Equations and Applications
  • Place of Presentation: 大阪府立大学I-siteなんば（大阪市）
  • Year and Date: 2016-07-24
  • Int'l Joint Research
• [Presentation] CONVERGENCE THEOREMS OF LINEAR CONTRACTIVE PROJECTIONS IN BANACH SPACES (2015)
  • Author(s): Takashi Honda and Shogo Kamino
  • Organizer: The Ninth International Conference on Nonlinear Analysis and Convex Analysis (NACA2015)
  • Place of Presentation: Rimkok Resort Hotel, Chiang Rai, THAILAND
  • Year and Date: 2015-01-21 – 2015-01-25
• [Presentation] The orthogonal decomposition of Banach spaces and its application to contractive semigroups (2013)
  • Author(s): Takashi Honda
  • Organizer: Operators on Banach Spaces
  • Place of Presentation: Castro Urdiales, Cantabria, Spain
• [Presentation] The orthogonal decomposition of Banach spaces and convergence theorems of a linear operator (2013)
  • Author(s): Takashi Honda
  • Organizer: The eighth international conference on Nonlinear Analysis and Convex Analysis (NACA2013)
  • Place of Presentation: 弘前大学（青森県）
• [Presentation] The Orthogonal Decomposition in Banach Spaces and Its Applications (2013)
  • Author(s): Takashi Honda
  • Organizer: The International Conference on Nonlinear Analysis and Optimization (ICNAO2013)
  • Place of Presentation: 國立中山大學, 高雄, 台湾
• [Presentation] On sums of cubes of primes and almost primes (2013)
  • Author(s): Koichi Kawada
  • Organizer: Analytic Number Theory
  • Place of Presentation: Mathematisches Forschungsinstitut Oberwolfach, Germany
• [Presentation] The ternary Goldbach problem --- from Hardy-Littlewood, Vinogradov to Helfgott (2013)
  • Author(s): Koichi Kawada
  • Organizer: 代数的整数論とその周辺
  • Place of Presentation: 京都大学数理解析研究所（京都府）