Frames and frame multiresolution analyses = 프레임과 프레임 MRA

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.
Advisors
Kim, Hong-Ohresearcher김홍오researcher
Publisher
한국과학기술원
Issue Date
1998
Identifier
144196/325007 / 000935298
Language
eng
Description

학위논문(박사) - 한국과학기술원 : 수학과, 1998.8, [ 59 p. ]

Keywords

MRA; Frame expansion; Wavelets; 웨이블릿; MRA; 프레임

URI
http://hdl.handle.net/10203/41803
Link
http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=144196&flag=t
Appears in Collection
MA-Theses_Ph.D.(박사논문)
Files in This Item
There are no files associated with this item.
  • Hit : 71
  • Download : 0
  • Cited 0 times in thomson ci

qr_code

  • mendeley

    citeulike


rss_1.0 rss_2.0 atom_1.0