一类方括号积多尺度分析的构造  

Construction of multiresolution analysis of bracket products

作　　者：冯祖针[1] 崔向照[1] 龙瑶[1] 

机构地区：[1]红河学院数学学院,云南蒙自661199

出　　处：《云南民族大学学报（自然科学版）》2013年第5期337-340,共4页Journal of Yunnan Minzu University:Natural Sciences Edition

基　　金：国家自然科学然金(11161020);云南省教育厅科学研究基金(2011Y297);红河学院博硕专项科研基金(10BSS135)

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.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.

关 键 词：方括号积 多尺度分析 多尺度逼近对 方括号积多尺度分析 基数B-样条 

分 类 号：O174.2[理学—数学]