2012 Fiscal Year Final Research Report
Linearity and topology of a sequence space determined by an Lp function
| Project/Area Number |
22540201
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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 | Kyushu Institute of Technology |
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Principal Investigator |
OKAZAKI Yoshiaki 九州工業大学, 大学院・情報工学研究院, 教授 (40037297)
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| Co-Investigator(Kenkyū-buntansha) |
HONDA Aoi 九州工業大学, 大学院・情報工学研究院, 准教授 (50271119)
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| Research Collaborator |
SATO Hiroshi 九州大学, 名誉教授
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| Project Period (FY) |
2010 – 2012
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| Keywords | 実解析 |
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| Research Abstract |
A new metric sequence space (Λp(f), dpf(a,b)) is derived from a single function f(≠0)∈Lp. Λp(f) is included in lp and realizes various interesting sequence spaces such as the Zygmund space l2(log l)s. But in general, Λp(f) is not linear and the explicit estimation as a sequence space is not clear. We investigate the linearity and the metric structure of Λp(f). We proved that mutual inclusion relation between Λp(f) and Λq(g) imply the metric inequality . Specifying the case to p=2, the linearity and the characterization as a sequence space of Λ2(f) is discussed by defining the doubling condition. By proving the upper and lower estimation of the metric d2f(a,b) by sequences, the linearity ofΛ2(f) is discussed by the doubling condition of a functionφf(x)=∫[0, x] α2|f～(α)|2dα, where f～is the Fourier transform.
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Research Products
(15 results)
