Frames and frame multiresolution analyses프레임과 프레임 MRA

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dc.contributor.advisorKim, Hong-Oh-
dc.contributor.advisor김홍오-
dc.contributor.authorLim, Jae-Kun-
dc.contributor.author임재근-
dc.date.accessioned2011-12-14T04:38:45Z-
dc.date.available2011-12-14T04:38:45Z-
dc.date.issued1998-
dc.identifier.urihttp://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=144196&flag=dissertation-
dc.identifier.urihttp://hdl.handle.net/10203/41803-
dc.description학위논문(박사) - 한국과학기술원 : 수학과, 1998.8, [ 59 p. ]-
dc.description.abstractThis 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.languageeng-
dc.publisher한국과학기술원-
dc.subjectMRA-
dc.subjectFrame expansion-
dc.subjectWavelets-
dc.subject웨이블릿-
dc.subjectMRA-
dc.subject프레임-
dc.titleFrames and frame multiresolution analyses-
dc.title.alternative프레임과 프레임 MRA-
dc.typeThesis(Ph.D)-
dc.identifier.CNRN144196/325007-
dc.description.department한국과학기술원 : 수학과, -
dc.identifier.uid000935298-
dc.contributor.localauthorKim, Hong-Oh-
dc.contributor.localauthor김홍오-
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MA-Theses_Ph.D.(박사논문)
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