DC Field | Value | Language |
---|---|---|
dc.contributor.advisor | Choi, Chang-Sun | - |
dc.contributor.advisor | 최창선 | - |
dc.contributor.author | Park, In-Sook | - |
dc.contributor.author | 박인숙 | - |
dc.date.accessioned | 2011-12-14T04:39:57Z | - |
dc.date.available | 2011-12-14T04:39:57Z | - |
dc.date.issued | 2005 | - |
dc.identifier.uri | http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=244491&flag=dissertation | - |
dc.identifier.uri | http://hdl.handle.net/10203/41882 | - |
dc.description | 학위논문(박사) - 한국과학기술원 : 응용수학전공, 2005.2, [ iii, 45 p. ] | - |
dc.description.abstract | This thesis is devoted to a study on the Fourier transform of Banach space valued functions defined on a locally compact abelian group. For a locally compact abelian(LCA) group $\mathbb{G}$ and 1 ≤ p ≤ 2, the Fourier type p norm with respect to \mathbb{G}$ of a bounded linear operator T from a Banach space to a Banach space is denoted by $\|T|\mathcal{FT}_p^{\mathbb{G}}\|$ and the class of T$satisfying $\|T|\mathcal{FT}_p^{\mathbb{G}}\|< ∞$ is denoted by $\mathcal{FT}_p^{\mathbb{G}}$. For 1<p≤ 2, we find a regular form of groups $\mathbb{G}$ which satisfies $\mathcal{FT}_p^{\mathbb{G}}=\mathcal{FT}_p^{\mathbb{T}}$, where $\mathbb{T}$ is the multiplicative group of all complex numbers of absolute value 1. Secondly, for 1< p≤2 and any infinite LCA group $\mathbb{G}$, we prove that $\|T|\mathcal{FT}_p^{\mathbb{G}}\|≤\|T|\mathcal{FT}_p^{\mathbb{A}}\|$ where $\mathbb{A}$ is the direct product of $\mathbb{Z}_2, \mathbb{Z}_3, \mathbb{Z}_4, …. If $\mathbb{G}$ is not of bounded order then $C\|T|\mathcal{FT}_p^{\mathbb{T}}\|≤\|T|\mathcal{FT}_p^{\mathbb{G}}\|$ for a positive constant $C$ dependent on $\mathbb{G}$ and $p$. And moreover $\|T|\mathcal{FT}_2^{\mathbb{G}}\|=\|T|\mathcal{FT}_2^{\mathbb{T}}\|$. If $\mathbb{G}$ is of bounded order then $\|T|\mathcal{FT}_p^{\mathbb{Z}_b^{∞}}\|≤ \|T|\mathcal{FT}_p^{\mathbb{G}}\|≤\|T|\mathcal{FT}_p^{\mathbb{Z}_d^{∞}}\|$ for some positive integers 2 ≤ b≤ d. From these results we obtain that if a Banach space has Fourier type p with respect to an infinite LCA group $\mathbb{G}$ for some 1<p≤ 2 then it is B-convex. In addition we obtain that, for any fixed infinite LCA group $\mathbb{G}$, a Banach space X has Fourier type 2 with respect to $\mathbb{G}$ if and only if X is isomorphic to a Hilbert space. | eng |
dc.language | eng | - |
dc.publisher | 한국과학기술원 | - |
dc.subject | Missing Data | - |
dc.subject | Hyper-EM | - |
dc.subject | Fourier transform | - |
dc.subject | 작용소 | - |
dc.subject | 푸리에 변환 | - |
dc.subject | Locally compact abelian group Missing Data | - |
dc.subject | Operator | - |
dc.subject | 국소 컴팩트 가환군lgorithm | - |
dc.title | (The) vector valued Fourier transform with respect to locally compact abelian groups and Hausdorff-Young | - |
dc.title.alternative | 국소 컴팩트 가환군에 대한 벡터 푸리에 변환과 Hausdorff-Young 부등식 | - |
dc.type | Thesis(Ph.D) | - |
dc.identifier.CNRN | 244491/325007 | - |
dc.description.department | 한국과학기술원 : 응용수학전공, | - |
dc.identifier.uid | 020005130 | - |
dc.contributor.localauthor | Choi, Chang-Sun | - |
dc.contributor.localauthor | 최창선 | - |
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