Some Problems On The Wavelet Expansions

In chapters1and2,we establish a characterization of Chui-Shi type for orthonormal wavelets in Sobolev spaces HS(R).In the third chapter, we show some new sufficient conditions and necessary conditions of Bessel sequences and Affine frames in Sobolev spaces.In the fourth chapter, we study the pointwise convergence of the multires-olution expansion in frequency spaces.