【摘要】 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.更多还原

【Abstract】 By the definition of multiresolution approximation of the Hilbert space,the properties of multiresolution approximation pairs are studied.Then a principle for constructing the multiresolution analysis of bracket products Vj and V-j is proposed based on a pair of compactly supported scaling functions φ and φ- of L2(R),whose relations satisfy the conditions of the bracket products.In addition,it gives a special bi-orthogonal and semi-orthogonal multiresolution analysis,which indicates that the multiresolution analysis of bracket products is more general.In particular,the method is applied to the cardinal B-spline to construct a multiresolution analysis of bracket products.Key words:bracket products; multiresolution analysis; multiresolution approximation pairs; multiresolution analysis of bracket products; cardinal B-spline更多还原