1996 Fiscal Year Final Research Report Summary
Theory of Paradistributions
| Project/Area Number |
06804007
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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 |
解析学
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| Research Institution | Kanazawa University |
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Principal Investigator |
HANZAWA Eiichi Kanazawa Univ., Faculty of Engineering, Associate Professor, 工学部, 助教授 (80142686)
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| Project Period (FY) |
1994 – 1996
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| Keywords | distribution / delta function |
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| Research Abstract |
The concept of paradistributions posed by Hanzawa in 1992 is a new class of generalized functions including. Schwarty distributions, in which the product of a Schwarty distribution and a paradistribution is always defined as a paradistribution.
Then, the product of finite Schwarty distributions are always defined as a paradistribution, so that the power of delta function are obtained in paradistributions.
The purpose of this research was, to construct a topology and a frame of Fourier analysis of paradistributions, for applications in physics, esphecially in the quantum field theory.
However, I could not find a natural topology and a natural frame of Fourier analysis.
After now, I plan to consider naive problem, e.g., on the product of Heaviside function and the delta function appeared in physics,
In the report, I pose a result, concerning soon equalities containing the power of delta functions, which are used in physics.
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