Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Point Values and Normalization of Two-Direction Multi-wavelets and their Derivatives

  • KEINERT, FRITZ (Department of Mathematics, Iowa State University) ;
  • KWON, SOON-GEOL (Department of Mathematics Education, Sunchon National University)
  • Received : 2015.10.31
  • Accepted : 2015.11.23
  • Published : 2015.12.23
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Abstract

A two-direction multiscaling function ${\phi}$ satisfies a recursion relation that uses scaled and translated versions of both itself and its reverse. This offers a more general and flexible setting than standard one-direction wavelet theory. In this paper, we investigate how to find and normalize point values and derivative values of two-direction multiscaling and multiwavelet functions. Determination of point values is based on the eigenvalue approach. Normalization is based on normalizing conditions for the continuous moments of ${\phi}$. Examples for illustrating the general theory are given.

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References

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