Mean value property and integrability for parabolic operators
| Project/Area Number |
15540163
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Nagoya University |
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Principal Investigator |
SUZUKI Noriaki Nagoya University, Graduate School of Mathematics, Associate Professor, 大学院・多元数理科学研究科, 助教授 (50154563)
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| Co-Investigator(Kenkyū-buntansha) |
MIYAKE Masatake Nagoya University, Graduate School of Math., Professor, 大学院・多元数理科学研究科, 教授 (70019496)
NISHIO Masaharu Osaka city Univ., School of Science, Associate Professor, 大学院・理学研究科, 助教授 (90228156)
SHIMOMURA Katsunori Ibaraki Univ., Dep.of Math, Associate Professor, 理学部, 助教授 (00201559)
石毛 和弘 名古屋大学, 大学院・多元数理科学研究科, 助教授 (90272020)
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| Project Period (FY) |
2003 – 2005
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| Project Status |
Completed (Fiscal Year 2005)
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| Budget Amount *help |
¥2,600,000 (Direct Cost: ¥2,600,000)
Fiscal Year 2005: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 2004: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2003: ¥900,000 (Direct Cost: ¥900,000)
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| Keywords | Bergman space / Bergman projection / parabolic operator / heat equation / mean value property / Bergman空間 / Gleason問題 / Toeplitz作用素 / Carleson測度 / 平均値の定理 / ベルグマン核 / 調和関数の可積分性 / 調和関数 / 再生核 |
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| Research Abstract |
In this period, we studied three subjects : (1) mean value density for temperatures, (2) structure of parabolic Bergman spaces, (3) polynomial solution for the heat equation.
(1) As for the mean value property, we discussed the existence of bounded mean value densities and the connection with the Dirichlet regularity. These results were published in Colloq.Math. 98 (2003), 87-98.
(2) We define the α-parabolic Bergman space and collected its basic properties in Osaka Math.J. 42 (2005), 106-133. For example, Huygens property, estimates of the fundamental solution, the duality relation and the explicit formula of the reproducing kernel. These results were extended to strip domains. We announced it at International Workshop of Potential Theory at Matsue (2004). The result will be published in ASPM in 2006. Last year, we dealt with the Gleason problem and the Toeplitz operators on parabolic Bergman spaces.
(3) We discussed the domain where the heat polynomial boundary value problem is solvable. The existence of such a doman is closely related to the zero sets of Hermite polynomials. We announced this result at the Second International Conference of Applied Mathematics at Provdiv, Bulgaria (2005).
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Report
(4 results)
Research Products
(19 results)
