1992 Fiscal Year Final Research Report Summary
Potential-kernels of logarithmic type and their applications
| 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)
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| Project Period (FY) |
1991 – 1992
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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 |
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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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