- M.Sc. Thesis Title: Wavelets
- Author: Bin Han
- Graduation/thesis year: June 1994.
- Supervisor: Professor Ruilin Long
- Location: Institute of Mathematics, Acdemia Sinica, Beijing, China
- Part I:
Dual wavelet frames.
- Part II:
MRA wavelets, Tilings and other results.
- MSC thesis in PDF file.
- Some results in my M.Sc. thesis were published.
See publication list.
Abstract of M.Sc. Thesis of Bin Han
In this thesis, we discuss some problems in wavelet
analysis. More precisely, the content of this paper
is the following:
In Part I, we present a complete description of dual wavelet
tight frames and by using these results, we construct dual
wavelet bases and dual wavelet tight frames in $L^2(R^n)$.
In Part II, we obtain a criterion for dual wavelet bases which
can be generated by an MRA. In Part III, we find a sufficient
and necessary condition for $T(\Gamma_0,M)$ to be a self-affine
tiling ( a kind of special wavelets) which is convenient to apply.
In the last Part IV, we show some results on shift-invariant space.
- On dual wavelet tight frames
- Some applications of projection operators in wavelets
- A sufficient and necessary condition on $\Gamma_0$ for
$T(\Gamma_0,M)$ to be a self-affine tiling
- Miscellaneous results on shift-invariant subspaces of