Spectral Gaps of the Dirac Operators with Periodic Point Interactions

• Project/Area Number: 20540182
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Tokyo Metropolitan University
• Principal Investigator: YOSHITOMI Kazushi Tokyo Metropolitan University, 大学院・理工学研究科, 准教授 (40304729)
• Project Period (FY): 2008 – 2010
• Project Status: Completed (Fiscal Year 2010)
• Budget Amount: ¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000); Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2009: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2008: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
• Keywords: 関数方程式 / ディラック作用素 / 周期ポテンシャル / 点相互作用 / スペクトラルギャップ / ディオファントス近似 / 非斉次近似定数

Research Abstract

In this research the one-dimensional Dirac operator with a periodic point interaction has been investigated. The main result gives a relationship between the asymptotic behavior of the length of the gaps and the Diophantine property of the parameters involved in the operator.

Research Products

• [Journal Article] Dirac operators with periodic point interactions-spectral gaps and inhomogeneous Diophantine approximation (2009)
  • Author(s): Kazushi Yoshitomi
  • Journal Title: Michigan Mathematical Journal 58 Pages: 363-384
• [Journal Article] Inverse spectral problems for singular rank-one perturbations of a Hill operator (2009)
  • Author(s): Kazushi Yoshitomi
  • Journal Title: Journal of the Australian Mathematical Society 87 Pages: 421-428
• [Journal Article] Dirac operators with periodic point interactions-spectral gaps and inhomogeneous Diophantine approximation (2009)
  • Author(s): 吉冨和志
  • Journal Title: Michigan Mathematical Journal 58
  • Peer Reviewed
• [Journal Article] Inverse spectral problems for singular rank-one perturbations of a Hill operator (2009)
  • Author(s): 吉冨和志
  • Journal Title: Journal of the Australian Mathematical Society 87 Pages: 421-428
  • Peer Reviewed
• [Journal Article] Dirac operators with periodic point interactions-spectralgaps and inhomogeneous Diophantine approximation (2009)
  • Author(s): 吉冨和志
  • Journal Title: Michigan Mathematical Journal (掲載受理済み)
  • Peer Reviewed
• [Journal Article] Inverse spectral problems for singular rank-oneperturbations of a Hill operator (2009)
  • Author(s): 吉冨和志
  • Journal Title: Journal of the Australian Mathematical Society (掲載受理済み)
  • Peer Reviewed
• [Presentation] Inverse scattering problems for singular rank-one perturbations of a selfadjoint operator. (2010)
  • Author(s): 吉冨和志
  • Organizer: 第49回実函数論函数解析学合同シンポジウム
  • Place of Presentation: 東京理科大学野田キャンパス
  • Year and Date: 2010-08-03
• [Presentation] Inverse scattering problems for singular rank-one perturbations of a selfadjoint operator. (2010)
  • Author(s): 吉冨和志
  • Organizer: The Jozef Marcinkiewicz Centenary Conference
  • Place of Presentation: Adam Mickiewicz University
  • Year and Date: 2010-06-29
• [Presentation] Inverse scattering problems for singular rank-one perturbations of a selfadjoint operator (2010)
  • Author(s): 吉冨和志
  • Organizer: 筑波ワークショップ
  • Place of Presentation: 筑波大学大学院数理物質科学研究科数学専攻
  • Year and Date: 2010-03-10
• [Presentation] Inverse scattering problemsfor singular rank-one perturbations of a selfadjoint operator (2010)
  • Author(s): 吉冨和志
  • Organizer: 第49回実函数論函数解析学合同シンポジウム
  • Place of Presentation: 東京理科大学野田キャンパス
• [Presentation] Inverse scatteringproblems for singular rank-one perturbations of a selfadjoint operator. (2010)
  • Author(s): 吉冨和志
  • Organizer: The Jozef Marcinkiewicz Centenary Conference
  • Place of Presentation: Adam Mickiewicz University
• [Presentation] Inverse scattering problemsfor singular rank-one perturbations of a selfadjoint operator. (2010)
  • Author(s): 吉冨和志
  • Organizer: 筑波ワークショップ
  • Place of Presentation: 筑波大学大学院数理物質科学専攻
• [Presentation] Inverse scattering problems for singular rank-one perturbations of a selfadjoint operator (2009)
  • Author(s): 吉冨和志
  • Organizer: 筑波大学解析セミナー
  • Place of Presentation: 筑波大学大学院数理物質科学研究科数学専攻
  • Year and Date: 2009-12-09
• [Presentation] Inverse scattering problems for singular rank-one perturbations of a selfadjoint operator (2009)
  • Author(s): 吉冨和志
  • Organizer: RIMS研究集会「スペクトル・散乱理論とその周辺」
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2009-12-03
• [Presentation] Inverse spectral problems for singular rank-one perturbations of a Hill operator (2009)
  • Author(s): 吉冨和志
  • Organizer: International Conference on Complex Analysis and Related Topics
  • Place of Presentation: University of Turku, Turku, Finland
  • Year and Date: 2009-08-17
• [Presentation] Inverse spectral problems for singular rank-one perturbations of a Hill operator (2009)
  • Author(s): 吉冨和志
  • Organizer: Sixth Advanced Course in Operator Theory And Complex Analysis
  • Place of Presentation: University of Sevilla, Sevilla, Spain
  • Year and Date: 2009-06-12
• [Presentation] Inverse spectra1 problems for singular rank one perturbations of a Hill operator (2009)
  • Author(s): 吉冨和志
  • Organizer: Third School and workshop on mathematical methods in quantum mechanics
  • Place of Presentation: Universita di Padova, Bressanone, Itary
  • Year and Date: 2009-02-16
• [Presentation] Inverse scattering problemsfor singular rank-one perturbations of a selfadjoint operator. (2009)
  • Author(s): 吉冨和志
  • Organizer: 筑波大学解析セミナー
  • Place of Presentation: 筑波大学大学院数理物質科学専攻
• [Presentation] Inverse scattering problemsfor singular rank-one perturbations of a selfadjoint operator. (2009)
  • Author(s): 吉冨和志
  • Organizer: RIMS研究集会「スペクトル・散乱理論とその周辺」
  • Place of Presentation: 京都大学数理解析研究所
• [Presentation] Inverse spectral problems for singular rank-one perturbations of a Hill operator. (2009)
  • Author(s): 吉冨和志
  • Organizer: International Conference on Complex Analysis and Related Topics
  • Place of Presentation: University of Turku, Finland
• [Presentation] Inverse spectral problems for singular rank-one perturbations of a Hill operator. (2009)
  • Author(s): 吉冨和志
  • Organizer: Sixth Advanced Course in Operator Theory and Complex Analysis
  • Place of Presentation: University of Sevilla, Spain
• [Presentation] Inverse spectral problems for singular rank-one perturbations of a Hill operator. (2009)
  • Author(s): 吉冨和志
  • Organizer: Third School and Workshop on Mathematical Methods in Quantum Mechanics
  • Place of Presentation: Universita di Padova, Bressanone, Itary
• [Presentation] Inverse spectral problems for singular rank one perturbations of a Hill operator (2008)
  • Author(s): 吉冨和志
  • Organizer: International conference on applied mathematics and approximation theory 2008
  • Place of Presentation: University of Memphis, USA
  • Year and Date: 2008-10-13
• [Presentation] Inverse spectral problems for singular rank-one perturbations of a Hill operator. (2008)
  • Author(s): 吉冨和志
  • Organizer: International Conference on Applied Mathematics and Approximation Theory
  • Place of Presentation: University of Memphis, USA