| Project/Area Number |
03452009
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| Research Category |
Grant-in-Aid for General Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
解析学
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| Research Institution | Nagoya University |
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Principal Investigator |
ITO Masayuki Nagoya University College of General Education Professor, 教養部, 教授 (60022638)
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| Co-Investigator(Kenkyū-buntansha) |
NAGAI Hideo General Education Associated Professor, 教養部, 助教授 (70110848)
IHARA Shunsuke General Education Associated, 教養部, 教授 (00023200)
SATO Ken-iti General Education Professor, 教養部, 教授 (60015500)
SUZUKI Noriaki General Education Assistant Professor, 教養部, 講師 (50154563)
MURAI Takafumi Nagoya University School of Sciences, College of Associated Professor, 理学部, 助教授 (00109266)
中野 伸 名古屋大学, 教養部, 講師 (40180327)
田中 和永 名古屋大学, 教養部, 講師 (20188288)
三宅 正武 名古屋大学, 教養部, 教授 (70019496)
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| Project Period (FY) |
1991 – 1992
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| Project Status |
Completed (Fiscal Year 1992)
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| Budget Amount *help |
¥4,700,000 (Direct Cost: ¥4,700,000)
Fiscal Year 1992: ¥2,200,000 (Direct Cost: ¥2,200,000)
Fiscal Year 1991: ¥2,500,000 (Direct Cost: ¥2,500,000)
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| Keywords | Hunt convolution kernels / kernels of logarithmic type / Spectral synthetic / Analytic capacity / non-integrability of sub-harmonic functions / resolvent of potential-kernels / recurrent semi-group / Ornstein-Uhlenbeck type process / 対数型ポテンシャル核 / 非回帰的半群 / 確率過程の再帰性 / 符号化定理 / 調和関数の境界挙動 / 偏微分方程式の可解性 / 周期軌道 |
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| Research Abstract |
By using some properties of potential-kernels of logarithmic type, we gave a definitive solution of the following well-known problem. "Does the totality of convolution kernels satisfying the domination principle coincide with the closure of the set of Hunt convolution kernels?" In this connection, we proved that a potential-kernel is spectral synthetic if it satisfies the domination principle. Applying to the theory of potential-kernels, we obtain that with a given potential-kernel satisfying the domination principle, its resolvent formed by nice potential-kernels is associated. Suggested by the sweeping-out process, we worked out an arc-variation to investigate the analytic capacity. In the study of the classical harmonic function theory, it is remarkable to determine domains on which non-zero subharmonic functions are not integrable.
Potential-kernels of logarithmic type possess recurrent semi-group,s which is closely related with the probability theory. In the study of the probability theory, we obtain a criterion of the transiency of Ornstein-Uhlenbeck type processes and results concerning optimal diffusion processes.
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