Some Results On Frame And Wavelet In H～s (R)

This thesis consists of five sections. The history of the related knowledge on frame and wavelet in L2(R) is presented in Section 1. Some results and preparing works are listed in Section 2. The major contents of this thesis are included in Section 3 to 5. In detail, we will prove in Section 3 that no collection of pure translations can form a frame for HS(R)(s > 0); Some results about frame sequence of translation will be given in Section 4; Characterization of an orthonormal wavelet basis in Hs(R)(s > 0) is established in last section.