一类方括号积多尺度分析的构造

Construction of multiresolution analysis of bracket products

根据Hilbert空间中多尺度逼近的定义,探讨了其上多尺度逼近对的性质.在此基础上,由L2(R)空间中1对满足方括号积关系的尺度函数φ和φ-,分析得到了构造方括号积多尺度分析Vj,V-j的方法,进一步讨论表明,双正交及半正交多尺度分析均为这类多尺度分析的特殊情形.特别地,将构造方法应用到基数B-样条,具体构造了1对具有一般性的方括号积多尺度分析.

By the definition of multiresolution approximation of the Hilbert space, the properties of multiresolution approximation pairs are studied. Then a principle for constructing the muhiresolution analysis of bracket products Vj and Vj is proposed based on a pair of compactly supported scaling functions φ and （φ of L2（R） ,whose relations sat- isfy the conditions of the bracket products. In addition,it gives a special bi - orthogonal and semi - orthogonal mul- tiresolution analysis, which indicates that the muhiresolution analysis of bracket products is more general. In parti- cular,the method is applied to the cardinal B - spline to construct a muhiresolution analysis of bracket products.