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半双正交小波Riesz基的构造及性质

The Construction and Properties of Semi-Biorthogonal Wavelet Riesz Bases
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摘要 根据方括号积多尺度分析对的基本理论,探讨了半双正交小波Riesz基的构造方法,并将该方法应用到基数B-样条,具体构造了一对半双正交样条小波Riesz基,同时研究了其支撑和对称性质. By the basic theory of bracket products multi-resolution analysis, the construction of semi-biorthogonal wavelet Riesz bases have been discussed. Then the method has been applied to the cardinal B-spline to construct a pair of semi-biorthogonal spline wavelet Riesz bases, and the support and symmetry are studied.
作者 冯祖针
机构地区 红河学院数学学院
出处 《红河学院学报》 2014年第2期24-26,共3页 Journal of Honghe University
基金 云南省应用基础研究计划项目(2013FZ118) 云南省应用基础研究计划青年项目(2012FD054) 云南省教育厅科学研究基金项目(2011Y297) 红河学院博硕专项科研基金项目(10BSS135)
关键词 方括号积 半双正交小波 基数B-样条 紧支撑 对称性 bracket products semi-biorthogonal wavelets cardinal B-spline compact support symmetry
分类号 O174.2 [理学—基础数学]
  • 相关文献

参考文献9

  • 1Daubechies I. Ten Lectures on Wavelets[M].Philadephia:SIAM,1992.
  • 2Chui C K,Wang J Z.On compactly supported spline wavelets anda duality principle[J].Trans Amer Math Soc,1992,330:903-916.
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  • 5Cohen A,Daubechies I. A stability criterion for bi-orthogonalwavelet bases and their related subband coding scheme[J].DukeMath J,1992,68:313-335.
  • 6Jia R Q,Wang J Z, Zhou D X.Compactly supported wavelet basesfor Sobolev spaces[J].Appl Comput Harmon Anal,2003,15(3):224-241.
  • 7冯祖针,崔向照,龙瑶.一类方括号积多尺度分析的构造[J].云南民族大学学报（自然科学版）,2013,22(5):337-340. 被引量：1
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二级参考文献9

  • 1DAUBECHIES I. Ten lectures on wavelets [ M ]. Philadel- phia: Society for industrial and applied mathematics, 1992.
  • 2COHEN A, DAUBECHIES I, FEAUVEAU J C. Biorthogonal bases of compactly supported wavelets [ J 3. Communications on Pure and Applied Mathematics, 1992, 45(5) : 485 -560.
  • 3COHEN A, DAUBECHIES I. A stability criterion for biorthogonal wavelet bases and their related subband coding scheme[J]. Duke Math J, 1992, 68(2) : 313 -335.
  • 4CHUI C K, WANG J. On compactly supported spline wavelets and a duality principle[ J ]. Transactions of the A- merican Mathematical Society, 1992, 330(2) : 903 -915.
  • 5CHUI C K, WANG J Z. A general framework of compactly supported splines and wavelets [ J ]. Journal of approxima- tion theory, 1992, 71(3). 263-304.
  • 6JIA R Q, WANG J, ZHOU D X. Compactly supported wavelet bases for Sobolev spaces[ J]. Applied and Compu- tational Harmonic Analysis, 2003, 15(3) : 224 -241.
  • 7JIA R Q, MICCHELLI C A. Using the refinement equa- tions for the construction of pre - wavelets II: Powers of two[J]. Curves and surfaces, 1991:209-246.
  • 8CHUI C K. An Introduction to Wavelets[ M]. 北京:人民邮电出版社,2009.
  • 9SCHOENBERG I J. Cardinal spline interpolation [ M ]. Philadelphia: Society for Industrial and Applied Mathe- matics, 1973.

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红河学院学报
2014年 第2期

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