2011 Fiscal Year Final Research Report
A study of harmonic analysis in orthogonal expansions
| Project/Area Number |
21540170
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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 | Kanazawa University |
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Principal Investigator |
KANJIN Yuichi 金沢大学, 機械工学系, 教授 (50091674)
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| Co-Investigator(Kenkyū-buntansha) |
SATO Shuichi 金沢大学, 学校教育系, 准教授 (20162430)
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| Co-Investigator(Renkei-kenkyūsha) |
TOHGE Kazuya 金沢大学, 電子情報系, 准教授 (30260558)
ARAI Hitosi 東京大学, 大学院・数理科学研究科, 教授 (10175953)
MIYACHI Akihiko 東京女子大学, 現代教養学部, 教授 (60107696)
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| Project Period (FY) |
2009 – 2011
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| Keywords | ハーディの不等式 / ペーリーの不等式 / 実ハーディ空間 / ラゲール展開 / エルミート展開 / ハンケル変換 / メーラー変換 |
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| Research Abstract |
We have obtained Hardy type inequalities for the Hermite expansion, the Laguerre expansions and the Mehler transforms, which are analogues of the classical Hardy inequality on the Hardy space. For Hermite and Laguerre expansions, the inequalities hold on the space of integrable functions. Also, the Paley type inequality for the Hankel transform has been obtained. Moreover, we have showed that the functions with positive Laguerre coefficients have the property that local square integrability at the origin implies global square integrability.
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