DC Field | Value | Language |
---|---|---|
dc.contributor.advisor | Kim, Hong-Oh | - |
dc.contributor.advisor | 김홍오 | - |
dc.contributor.author | Lim, Jae-Kun | - |
dc.contributor.author | 임재근 | - |
dc.date.accessioned | 2011-12-14T04:38:45Z | - |
dc.date.available | 2011-12-14T04:38:45Z | - |
dc.date.issued | 1998 | - |
dc.identifier.uri | http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=144196&flag=dissertation | - |
dc.identifier.uri | http://hdl.handle.net/10203/41803 | - |
dc.description | 학위논문(박사) - 한국과학기술원 : 수학과, 1998.8, [ 59 p. ] | - |
dc.description.abstract | This thesis is devoted to a study of an abstract theory of frames and frame multiresolution analysis. First, we give two equivalent conditons for a frame to be a Riesz basis of a separable Hilbert space by a careful examination of the ``projection method`` which approximates the coefficients of a frame expansion, and obtain formulas of Riesz bounds in terms of the eigenvalues of the Gram matrices of finite subsets of a frame. We then generalize bi-orthogonal (non-orthogonal) MRA to frame MRA in which the family of integer translates of a scaling function forms a frame for the initial ladder space $V_0$. We probe the internal structure of frame MRA``s and establish the existence of a dual scaling function, and show that, unlike bi-orthogonal MRA, there exists a frame MRA that has no ``wavelet.`` We prove the existence of a dual wavelet under the assumption of the existence of a wavelet and present easy sufficient conditions for the existence of a wavelet. Finally, we give a new proof of an equivalent condition for the translates of a function in $L^2(R)$ to be a frame of its closed linear span, and present a proof that, among all complex numbers, Duffin-Schaeffer``s choice in the Neumann series expansion of the inverse of a frame operator has the best possible convergence rate. | eng |
dc.language | eng | - |
dc.publisher | 한국과학기술원 | - |
dc.subject | MRA | - |
dc.subject | Frame expansion | - |
dc.subject | Wavelets | - |
dc.subject | 웨이블릿 | - |
dc.subject | MRA | - |
dc.subject | 프레임 | - |
dc.title | Frames and frame multiresolution analyses | - |
dc.title.alternative | 프레임과 프레임 MRA | - |
dc.type | Thesis(Ph.D) | - |
dc.identifier.CNRN | 144196/325007 | - |
dc.description.department | 한국과학기술원 : 수학과, | - |
dc.identifier.uid | 000935298 | - |
dc.contributor.localauthor | Kim, Hong-Oh | - |
dc.contributor.localauthor | 김홍오 | - |
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