Some formulas induced by calculations of reproducing kernels and its applkications

• Project/Area Number: 18540186
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Saga University
• Principal Investigator: FUJITA Keiko Saga University, 文化教育学部, 准教授 (40274568)
• Project Period (FY): 2007 – 2008
• Project Status: Completed (Fiscal Year 2008)
• Budget Amount: ¥3,910,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥510,000); Fiscal Year 2008: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2007: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2006: ¥1,700,000 (Direct Cost: ¥1,700,000)
• Keywords: 再生核 / 積分公式 / 正則関数 / 調和関数 / 二重級数

Research Abstract

ノルムを用いて定義された幾つかの球状の領域に対して、二重級数展開式で表示されたセゲー核の無限和の幾つかが2次元の場合には計算でき、具体的な式で与えることができた。また、上記の球状領域上の調和関数に対してはコーシー核を用いたの積分公式を考察し、コーシー核を利用して調和関数の解析接続に関する定理を証明した。その後、考察していた領域の境界がリー球の部分空間の和集合として表示できることが分かり、積分を重積分の形で表示することで、境界上での積分による別の積分表示を考えた。

Research Products

• [Journal Article] Integral representations for holomorphic functions on some balls (2009)
  • Author(s): K. Fujita
  • Journal Title: Proceedings of the 16th International conference on finite or infinite dimensional complex analysis and applications Pages: 93-98
• [Journal Article] Reproducing kernels for holomorphic functions on some balls related to the Lie ball (2009)
  • Author(s): K. Fujita
  • Journal Title: Ann. Polo. Math 91.2-3 Pages: 219-234
  • Peer Reviewed
• [Journal Article] Reproducing Kernels for Harmonic Functions on Some Balls, FURTHER PROGRESS IN ANALYSIS (2008)
  • Author(s): K. Fujita
  • Journal Title: Proceedings of the 6th International ISAAC Congress Pages: 567-574
  • Peer Reviewed
• [Journal Article] Integral representations on some balls related to the Lie ball (2008)
  • Author(s): K. Fujita
  • Journal Title: Proceedings of international symposium on new development of geometric function theory and its applications, School of mathematical sciences faculty of science & technology university Kebangsaan Malaysia Pages: 110-117
• [Journal Article] Topics on the Bergman kernel for some balls, Proceedings of the 5th International ISAAC Congress (2008)
  • Author(s): K. Fujita
  • Journal Title: World Scientific publishers Pages: 125-135
  • Peer Reviewed
• [Journal Article] Bergman kernels and Szego kernels for some balls related to the Lie ball, Function Spaces in Complex and Clifford Analysis (2008)
  • Author(s): K. Fujita
  • Journal Title: National University Publishers Hanoi Pages: 79-89
  • Peer Reviewed
• [Journal Article] Topics on the Bergman kernel for some balls (2008)
  • Author(s): K. Fujita
  • Journal Title: Proceedings of the 5th International ISAAC Congress, World Scientific publishers Pages: 125-135
  • Peer Reviewed
• [Journal Article] Topics on the Bergman kernel for some balls (2008)
  • Author(s): K. Fujita
  • Journal Title: Proceedings of the 5th International ISAAC Congress, World Scientific publishers 無
  • Peer Reviewed
• [Journal Article] Integral representationson some balls related to the Lie ball (2008)
  • Author(s): K. Fujita
  • Journal Title: Proceedings of international symposiumon new development of geometric function theory and its applications 無
• [Journal Article] Reproducing Kernels for Harmonic Functions on Some Balls (2008)
  • Author(s): K. Fujita
  • Journal Title: FURTHER PROGRESS IN ANALYSIS, Proceedings of the 6th International ISAAC Congress 無
  • Peer Reviewed
• [Journal Article] Bergman kernels and Szego kernels for some balls relates to the Lie ball (2008)
  • Author(s): Keiko Fujita
  • Journal Title: Function Spaces in Complex and Clifford Analysis Pages: 79-89
  • Peer Reviewed
• [Journal Article] Reproducing kernels for holomorphic functions on some balls related to the Lie ball (2007)
  • Author(s): Keiko Fujita
  • Journal Title: Ann.Polo.Math. 91.2-3 Pages: 219-234
  • Peer Reviewed
• [Journal Article] Topics on the Bergman kernel for some balls (2007)
  • Author(s): Keiko Fujita
  • Journal Title: Proceedings of the 5th International ISAAC Congress, World Scientific publishers (in printted)
• [Journal Article] Reproducing kernels for holomorphic functions on some balls related to the Lie ball (2007)
  • Author(s): Keiko Fujita
  • Journal Title: Ann. Polo. Math (to appear)
• [Presentation] Integral representations on some balls related to the Lie ball (2008)
  • Author(s): K. Fujita
  • Organizer: International symposium on new development of geometric function theory and its applications, Social Security Training Institute (ESSET)
  • Place of Presentation: Selangor Malaysia
  • Year and Date: 2008-11-11
• [Presentation] Integral representations on some balls related to the Lie ball (2008)
  • Author(s): K. Fujita
  • Organizer: International symposium on new development of geometric function theory and its applications
  • Place of Presentation: Social Security Training Institute (ESSET), Selangor Malaysia
  • Year and Date: 2008-11-11
• [Presentation] Integral representations for holomorphic functions on some balls (2008)
  • Author(s): K. Fujita
  • Organizer: The 16^th International conference on finite or infinite dimensional complex analysis and applications, Dongguk University
  • Place of Presentation: Gyeongju, Korea
  • Year and Date: 2008-07-28
• [Presentation] Integral representations for holomorphic functionson some balls (2008)
  • Author(s): K. Fujita
  • Organizer: The 16^<th> International conference on finite or infinite dimensional complexanalysis and applications
  • Place of Presentation: Dongguk University, Gyeongju, Korea
  • Year and Date: 2008-07-28
• [Presentation] Reproducing kernels for harmonic functions on some balls (2007)
  • Author(s): K. Fujita
  • Organizer: 6th ISAAC Congress, Middle east technical university
  • Place of Presentation: Ankara Turkey
  • Year and Date: 2007-08-15
• [Presentation] Reproducing kernels for harmonic functions on some balls (2007)
  • Author(s): Keiko Fujita
  • Organizer: 6th ISAAC Congress
  • Place of Presentation: Middle east technical university, Ankara Turkey
  • Year and Date: 2007-08-15
• [Presentation] Remark on the Fourier-Borel transformation on some varieties (2007)
  • Author(s): Keiko Fujita
  • Organizer: 15^th International conference on finite or infinited dimensional complex analysis and applications
  • Place of Presentation: Osaka City University,Osaka
  • Year and Date: 2007-07-31
• [Presentation] Holomorphic functions on some balls related to the Lie ball (2006)
  • Author(s): K. Fujita
  • Organizer: The International Symposium on Complex Function Theory and Applications, Transilvania University
  • Place of Presentation: Brasov, Romania
  • Year and Date: 2006-09-05
• [Presentation] Bergman kernels and Szego kernels for some balls related to the Lie ball (2006)
  • Author(s): K. Fujita
  • Organizer: The 14-th International conference on finite or infinite dimensional complex analysis and applications, Hue University
  • Place of Presentation: Vietnam
  • Year and Date: 2006-08-01
• [Presentation] Reproducing kernels for holomorphic functions on some balls related to the Lie ball (2006)
  • Author(s): K. Fujita
  • Organizer: International Summer School in Several Complex Variables
  • Place of Presentation: Szczyrk, Poland
  • Year and Date: 2006-06-20