An Application of Continuous Wavelet Transform in Differential Equations

  • Qu Han-zhang
  • Xu Chen
  • Zhao Ruizhen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2251)


The relation between some differential equations and the integral equations is discussed; the differential equations can be transformed into the integral equations by using the continuous wavelet transform; the differential equations and the integral equations are equivalent not only in the weak topology but also in the strong topology; the discussion on the differential equations can be connected with the discussion on the integral equations.


Integral Equation Integral Operator Bilinear Form Discret Wavelet Bounded Linear Operator 
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    Ingrid Daubechies. Ten Lectures on Wavelets. Philadelphia. Pennsyvania: Society for Industrial and Applied Mathematics. 1992Google Scholar
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    Zheng Wei-xing, Wang Sheng-wang. Outline of real function and functional analysis. Academical Education Press, China. 1991Google Scholar
  3. 3.
    Song Guo-xiang. Numerical Analysis and Introduction to Wavelet. Science and Technology Press of Henan, China. 1993Google Scholar
  4. 4.
    Charles K. Chui. An Introduction to Wavelets. Academic Press. Inc. 1992Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Qu Han-zhang
    • 1
  • Xu Chen
    • 2
  • Zhao Ruizhen
    • 3
  1. 1.Xi’an Post and Telecommunications InstituteXi’anP. R. China
  2. 2.Xidian UniversityXi’anP. R. China
  3. 3.Shenzhen UniversityP. R. China

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