Acta mathematica scientia,Series A ›› 2013, Vol. 33 ›› Issue (1): 89-97.

• Articles • Previous Articles     Next Articles

A Note on Wavelet Frames for Affine Subspaces of L2(Rd)

 ZHOU Feng-Ying1, LI Yun-Zhang2*   

  1. 1.School of Science, East China Institute of Technology, Nanchang 330013;
    2.College of Applied Sciences, Beijing University of Technology, Beijing |100124
  • Received:2011-03-11 Revised:2012-08-17 Online:2013-02-25 Published:2013-02-25
  • Contact: LI Yun-Zhang|yzlee@bjut.edu.cn E-mail:yzlee@bjut.edu.cn
  • Supported by:

    国家自然科学基金(11271037)、北京市自然科学基金(1122008)和北京市教育委员会科技计划面上项目(KM201110005030)资助

Abstract:

This paper addresses the construction of wavelet frames in the setting of finitely generated affine subspaces of L2(Rd). It is proved that an arbitrary finitely generated affine subspace admits a Parseval wavelet frame with finitely many generators. A sufficient condition is obtained for an affine subspace to be a reducing subspace. For a class of affine subspaces generated by a single function whose Fourier transform is a characteristic function, we derive an explicit Fourier-domain expression of the projection operators related to the construction of wavelet frames. Some examples are also provided.

Key words: Affine subspace, Parseval frame, Wavelet frame

CLC Number: 

  • 42C15
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