Study on vector bundles induced by module structure of reproducing kernel Hilbert spaces consisting of multivariable analytic functions

• Project/Area Number: 23740106
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Basic analysis
• Research Institution: Shimane University
• Principal Investigator: SETO Michio 島根大学, 総合理工学研究科(研究院), 准教授 (30398953)
• Project Period (FY): 2011 – 2013
• Project Status: Completed (Fiscal Year 2013)
• Budget Amount: ¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000); Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2011: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
• Keywords: 再生核ヒルベルト空間 / ハーディ空間 / 多変数作用素論 / グラフ理論 / 再生核 / 合成作用素 / ディリクレ空間 / 国際情報交流 / ヒルベルト加群

Research Abstract

1. A certain class of self-adjoint operators is induced by submodules of the Hardy space over the bidisk. These operators are called defect operators. We studied eigenvalues and eigenfunctions of defect operators perturbed by biholomorphic maps.
2. A class of reproducing kernel Hilbert spaces can be constructed from graphs by a canonical way. We studied relation between their Gram matrices and Laplace matrices. Further, we introduced de Branges-Rovnyak theory into graph theory, and showed that it would be an appropriate framework dealing with graph homomorphisms.

Research Products

• [Journal Article] Gram matrices of reproducing kernel Hilbert spaces over graphs (2014)
  • Author(s): Seto Michio, Suda Sho, Taniguchi Tetsuji
  • Journal Title: Linear Algebra Appl Volume: 445 Pages: 56-68
  • NAID: 120005497076
  • Peer Reviewed
• [Journal Article] Gram matrices of reproducing kernel Hilbert spaces over graphs (2014)
  • Author(s): Michio Seto, Sho Suda and Tetsuji Taniguchi
  • Journal Title: Linear Algebra and its Applications Volume: 445 Pages: 56-58
  • NAID: 120005497076
  • Peer Reviewed
• [Journal Article] A perturbation theory for core operators of Hilbert-Schmidt submodules in $H^2({￥mathbb D)^2)$ (2011)
  • Author(s): Seto Michio
  • Journal Title: Integral Equations Operator Theory Volume: 70, no.3 Pages: 379-394
  • Peer Reviewed
• [Journal Article] A perturbation theory for core operators of Hilbert-Schmidt submodules in $H^2({\mathbb D}^2)$ (2011)
  • Author(s): Michio Seto
  • Journal Title: Integral Equations and Operator Theory Volume: 70 Pages: 379-394
  • Peer Reviewed
• [Presentation] Graph homomorphisms and de Branges-Rovnyak theory (2014)
  • Author(s): Michio Seto
  • Organizer: Hakata Workshop 2014 Discrete Mathematics and its Applications
  • Place of Presentation: リファレンス駅東ビル(福岡市)
  • Year and Date: 2014-02-08
• [Presentation] 再生核ヒルベルト空間のグラフ理論への応用について (2013)
  • Author(s): 瀬戸 道生
  • Organizer: 第22回関数空間セミナー
  • Place of Presentation: 東京理科大学
  • Year and Date: 2013-12-21
• [Presentation] Hardy 空間の加群構造に現れるKrein 空間について (2013)
  • Author(s): 瀬戸 道生
  • Organizer: 2013年度関数環研究集会
  • Place of Presentation: クロスパル新潟(新潟市)
  • Year and Date: 2013-12-12
• [Presentation] Dirichlet 空間と作用素論2 (2012)
  • Author(s): 瀬戸 道生
  • Organizer: 2012年度関数環研究集会
  • Place of Presentation: 日本大学理工学部
  • Year and Date: 2012-11-12
• [Presentation] 再生核ヒルベルト空間とそのdefect 作用素について (2012)
  • Author(s): 瀬戸 道生
  • Organizer: 第51回実函数論・函数解析学合同シンポジウム
  • Place of Presentation: 東京理科大学
  • Year and Date: 2012-08-06
• [Presentation] Operators induced by the reproducing kernel of the Dirichlet space (2011)
  • Author(s): Michio Seto
  • Organizer: Research on preserver problems concerning to Banach algebras and its applications
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2011-10-31
• [Presentation] A perturbation theory for defect operators of Hilbert-Schmidt submodules (2011)
  • Author(s): Michio Seto
  • Organizer: PARC Workshop 2011 Operator Theory and Its Applications
  • Place of Presentation: Seoul National University
  • Year and Date: 2011-06-17
• [Presentation] Hardy空間の加群構造に現れれるKrein空間について
  • Author(s): 瀬戸 道生
  • Organizer: 2013年度関数環研究集会
  • Place of Presentation: クロスパル新潟（新潟市）
• [Presentation] 再生核ヒルベルト空間のグラフ理論への応用について
  • Author(s): 瀬戸 道生
  • Organizer: 第22回関数空間セミナー
  • Place of Presentation: 東京理科大学神楽坂校舎
• [Presentation] Graph homomorphisms and de Branges-Rovnyak theory
  • Author(s): Michio Seto
  • Organizer: Hakata Workshop 2014 Discrete Mathematics and its Applications
  • Place of Presentation: リファレンス駅東ビル（福岡市）
• [Presentation] 再生核ヒルベルト空間とその defect 作用素について
  • Author(s): 瀬戸 道生
  • Organizer: 第51回 実函数論・函数解析学合同シンポジウム
  • Place of Presentation: 東京理科大学（東京都）
  • Invited