Wavelet Generators Of C_u(R～2)

Many results have been obtained about the construction and decomposition of wavelets in L2(R). In 1996, Charles K.Chui and Chun Li studied the construction and decomposition of wavelets in the space of bounded uniformly continuous functions on R. But many applications employ two-dimensional situation. In this thesis, by the introduction of interpolating multiresolutionanalysis related to the matrix M = , we give two stable waveletgenerators in the space of bounded uniformly continuous functions on R2.This thesis is organized as follows. In Chapter 1, some necessary notations and definitions, the background and the main results of this thesis are given; The definition of an interpolating multiresolution is simplified, and some examples are provided in Chapter 2; In Chapter 3 ,two stable generators of an interpolating multiresolution are constructed in the space of bounded uniformly continuous functions on R2 ; Two stable generators of the corresponding wavelet space are obtained in last Chapter .