| Project/Area Number |
22540166
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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 | Hirosaki University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
NAKAI Eiichi 茨城大学, 理学部数学・情報数理領域, 教授 (60259900)
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| Project Period (FY) |
2010 – 2012
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| Project Status |
Completed (Fiscal Year 2012)
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| Budget Amount *help |
¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2011: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 多重フーリエ級数 / 級数の点毎収束 / 重み付き格子点問題 / Gibbs-Wilbraham 現象 / Pinsky 現象 / 波動方程式の基本解 / Mathematica(ソフト) / 実関数論 / Gibbs-Wilbraham現象 / Pinsky現象 / 点毎収束 / 曲線の長さ / Szegoの方法 |
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| Research Abstract |
For the multiple Fourier series of periodization of radial functions on d-dimensional Euclidean space, we studied the behavior of the spherical partial sum. We showed the Gibbs-Wilbraham phenomenon, the Pinsky phenomenon and the third phenomenon for the multiple Fourier series. The third phenomenon is closely related to the lattice point problems, which is classical theme of analytic number theory. We also proved that the convergence problems on the Fourier series is equivalent to the lattice point problems in a sense.
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