A Class Of Cardinal Orthogonal Scaling Functions

This thesis consists of six sections. The history of sampling theorem in wavelet subspaces is presented in section 1. Some results and preparing works are showed in section 2. There is the major content of this thesis from the third section to the sixth. In detail, a class of cardinal orthogonal scaling functions, which are abbreviated as COSF, are constructed in the third section, and are proved that they have the properties of decay; In the fourth section, the regularities of these COSF are studied in the generalized condition; Under the two special cases, the regularities and the decays of these COSF are discussed in the fifth and sixth sections, respectively.